Dr. Dimitris Bertsimas

About Me

I’m the current Associate Dean of Business Analytics, Boeing Professor of Operations Research and faculty director of the Master of Business analytics at MIT. I received my SM and PhD in Applied Mathematics and Operations Research from MIT in 1987 and 1988 respectively. I have been MIT faculty since 1988. My research interests include optimization, machine learning and applied probability and their applications in health care, finance, operations management and transportation. I have co-authored more than 200 scientific papers and four graduate level textbooks.

I am the editor in Chief of INFORMS Journal of Optimization and former department editor in Optimization for Management Science and in Financial Engineering in Operations Research. I am also a member of the National Academy of Engineering since 2005, an INFORMS fellow, and have received numerous research awards including the Morse prize (2013), the Pierskalla award for best paper in health care (2013), the best paper award in Transportation (2013), the Farkas prize (2008), the Erlang prize (1996), the SIAM prize in optimization (1996), the Bodossaki prize (1998) and the Presidential Young Investigator award (1991-1996).

I have consulted widely in a variety of industries and have cofounded several very successful companies. In 1999, I co-founded Dynamic Ideas, LLC, which developed machine learning methods for asset management. In 2002, the assets of Dynamic Ideas were sold to American Express. From 2002-2010, I was the head of the quantitative asset management group of Ameriprise Financial, responsible for $12 billion of assets. In 2001, I cofounded D2 Hawkeye, a data mining health care company and responsible for its machine learning capabilities. The company was sold to Verisk Health in 2009. In 2011 I cofounded Benefits Science Technologies LLC, a company that designs health care benefits, Savvi Financial LLC, a financial advice company and Alpha Dynamics LLC, an asset management company. In 2015 I cofounded P2 Analytics LLC, a consulting company and in 2018 Interpretable AI, a machine learning company.

My Philosophy
Path, philosophy and aspirations

This document outlines my philosophy and values as an advisor and more generally in life. My hope is that younger generations, particularly my students and their students, will benefit by considering these thoughts.

We live rather limited life spans and I feel that for our lives to have a meaning we should all consider the question of what is important in life. Different people may give different answers, but I think it is critical, for every one of us to attempt to answer the question.

What is Important in Life?
This is a question that has occupied my mind for a long time. My experiences have led me to define what I consider important in life:

  1. To improve the human condition.
  2. To positively affect the lives of people, especially young people.
  3. To increase the human understanding of how the world works.

My path
My life path, sometimes intentionally, sometimes accidentally has led me to seek to achieve these objectives through science. I have been associated with educational institutions all my life, the first 25 years as a student and the last 27 years as a university professor. The key methods I have been using are:

  1. Scientific research
  2. Education
  3. Building companies

Scientific Research
As I reflect back on my life, the one thing I am very proud of is my graduate students. When I meet them they are typically in their early twenties, they have been among the very best in their undergraduate institutions, with high aspirations, exceptional ability, various degrees of maturity, a bit inexperienced, without often a clear vision of their future and direction. Not too different from the way I was at their age. It has been my great privilege and joy to serve as their advisor. I consider being the advisor of my graduate students far and away the most important aspect of my life as an academic. My graduate students have been and continue to be my first priority.

What do I aspire to help them learn?
The superficial objective is to teach them the principles of Operations Research, my area of expertise. I feel this is the minimal and not a particularly important objective. The most important thing I aspire to help them learn is why research is important and especially what research is important.

In my opinion, research is serious business and is linked to what is important in life I outlined earlier. The key principles in research in my mind are:

  1. Research can change the world.
  2. There is nothing that we cannot achieve if we put our minds into it.
  3. The only research worth doing has the following characteristic: Assume we succeed 100% in answering the research question we aim to address. Then, does something change in the world for the better among those things that are important in life? That is, does the human condition improve? Do the results of the research affect what we teach the future generations? Does the research increase the understanding of how the world works? If the answer to these questions is no, and in my experience it often is, then I do not think we should be doing this research on the first place. What is important is that these questions are answerable before we do the research.

It took me more than a decade to fully crystalize these principles. I see a lot of people, including myself in my early years, who aim to impress rather than change the world. More than the specific areas of research, my central aspiration is to help my graduate students learn these principles.

Education
I have been privileged to be at MIT, a world class research university, since my early twenties. It is my aspiration to generate new knowledge that I consider important in life and teach the next generations by introducing new classes and writing books. I also believe that this responsibility is increasing with age, that is as the depth of my understanding and experience increases, I feel an increased sense of responsibility to transmit the understanding and experience I have achieved to help the young generation.

Entrepreneurship
I have been a serial entrepreneur in the last 20 years, and I intend to continue to do it with increasing intensity until I cannot do it anymore. Given my love of being a university professor, it is reasonable to ask why.

I believe that research and education can affect the human condition and influence a limited number of human lives. It is possible that others can take the research ideas scientists generate and create significant impact. My observation, however, is that the limited number of scientists who have produced research that is capable of affecting the lives of millions of people created the companies themselves. It is my belief that the major way to affect the human condition in large scale is to build a successful company. From my experience, the only way to build a successful company is to inspire a team of people, create a common vision and execute the vision successfully.
Money is not my primary motivation. I see money as an enabler for changing the world, as a consequence of being successful in changing the world, but not as the primary objective. In fact, I agree with Steve Jobs: "My aspiration was never to be the richest person in the cemetery," even though he is in fact.

Values and principles
In the first half a century of life, I have formed a system of beliefs and values. I have tried to conduct my life in accordance to these principles. I aspire to continue to use these principles in all aspects of my life:

  1. Merit should guide decisions. MIT is by and large a meritocracy, and to a large degree, in my opinion, the reason it became a world-­‐class institution during the 20th century. In my experience, merit in the end carries the day and the best way to achieve a merit based environment is to encourage an open ideas environment. In my experience, the best idea should be followed, not whose idea it was.
  2. Integrity matters. I learned from my father that honesty and the truth are how one should contact his/her life even if sometimes it is inconvenient. I feel it is important to do what you say and, independent of contracts and agreements, your word should matter.
  3. High aspirations matter. We should aim to change the world, if we have a chance to do it. I do not know of many examples of people who changed the world without aiming to do so.
  4. Be a master of your destiny. All my life I have tried to be in a position that I can affect my future. I have always put more weight on my own beliefs. I have also tried to form beliefs independently, judge people and ideas on their merits.
  5. Surround yourself with exceptional people. In my experience, first rate people surround themselves with other first rate people, but second rate people surround themselves with third rate people. In my experience, one cannot succeed to change the world alone. A superb team is necessary.
  6. Good judgment is critical. In my experience, there are few important decisions in life that have a first order effect in our trajectory and impact. Exhibiting good judgment during these decisions can affect our lives to the first order.
  7. Loyalty matters. I have tried to be loyal to the people who are close to me, especially my students. They have entrusted their future in my hands and I take this responsibility very seriously. I have also experienced that loyalty is reciprocated.
  8. Positive reinforcement. Especially with young people, it is critical to give them positive reinforcement: an encouraging word, a positive comment goes a long way to empower very talented but a bit uncertain young people to achieve their potential.

Life Stories

What follows is an excerpt from a speech made to a recent graduating class:

As a speaker today I chose to tell you three stories from my life that affected it and taught me something that I think may be of some value to you.

The first story is about death.

I am the only child of a middle class Greek family. I was raised in Athens Greece, where I finished high school and university before coming to MIT in 1985 as a doctoral student. My mother was an elementary school teacher and my father was an engineer. I was always very close to my parents, and despite the long distance between Boston and Athens, I saw my parents twice a year for Christmas and summer. I was particularly close to my father. In March of 2007 I received a phone call from my cousin that my father had gastric cancer. I immediately arranged for my father to have surgery from the best Greek surgeon on these matters that was arranged for early April of 2007. The night before the surgery the surgeon told me and my wife Georgia that while he was optimistic about my father, there was a possibility that the cancer might have spread outside the stomach area, in which case, he was not going to continue the operation. The next day, half an hour after the surgery started, the surgeon came out and told me that the cancer has spread and he would not continue the operation. For the first time in my life I could not speak for several minutes as I knew what this meant. I arranged for my father to come to Boston and to do chemotherapy at the Massachusetts General hospital on the other side of the river visible from here. My parents stayed for six months, my father responded well to chemotherapy, and in October 2007, they went back to Greece. My father had a good year. Unfortunately after a year, in October 2008 his condition worsened as the cancer started to grow again, and passed away in March 2009 almost two years from diagnosis. The following month, the sister of my mother, my only aunt, who was very close to my family, passed away, and in the August of 2009, my mother passed from complications of diabetes. My mother as well as my aunt had diabetes for a significant part of their adult lives. In a span of five months in 2009 I lost three out of the four people in the world I have been closest to.

I have always been interested in medicine, but this experience led me to initiate a research program in personalized medicine, under which the treatment of a patient is adjusted to the genomic and phenotype characteristics of the patient. It is with some pride that together with 3 of my students, we won the first prize in healthcare from INFORMS (the professional society I belong) for a paper we wrote about gastric cancer that was inspired by my father’s illness. And earlier this year, a paper on personalized diabetes management inspired by my mother’s illness with another 3 of my students was published in Diabetes Care, the top journal for diabetes in the world. Today, more than half my research group are working on their PhD in personalized medicine with the aspiration to affect the practice of medicine and using analytics, especially Machine learning, to make it more effective. Overcoming the sadness of losing 3 of the closest people in my life and transforming a very difficult experience to a positive outcome, has made the journey and my life more meaningful and worthwhile.

My second story is about aspirations.

The normal duration of studies in the department of EECS of National Technical University of Athens, where I studied is five years. You have to take 60 classes in order to graduate. So naturally, nobody has ever attempted to graduate in less than five years. With the objective to find my boundaries, I set a goal of doing exactly that despite the advice of my father not to do it as I may compromising my grades and that might have an effect on being admitted on a top doctoral program, which has always been my goal. With lot of dedication and positive energy, I finished my studies in four years and was accepted as a doctoral student at the department of applied mathematics at MIT in 1985. When I came to the mathematics department at MIT I learnt about the Operations Research Center and I loved it. So I decided to try to finish a PhD in both programs and try to do it in 3 years. Again with dedication and positive energy, I finished my studies in 1988, the year I joined the Sloan school as an assistant professor. In the summer of 1989, as an assistant professor I set a goal to prove that a central algorithm in optimization was faster than previously thought possible. This would have been a major research development. We were moving houses that summer and my wife complains that I did not help in the move as the proof was coming any minute. In the end I did not succeed in this goal, but my understanding of optimization deepened considerably. As a professor, I have tried to teach my students to aim high, even higher that they think they can achieve and dedicate themselves to achieve it. I have observed both from my personal experience as well as from the experience of my students that those that have a positive orientation towards the goals they set typically achieve them. In fact, it has been my experience that the most important quality for determining success in life, more than IQ or EQ is positive energy, the belief that you will succeed in whatever you set out to achieve. It is exactly this belief that I hope we installed in you, which I hope will be with you for the rest of your life.

My final story is about love.

From as long as I remember, I wanted to become a professor in a leading research university. I did not know very well what a research university was, and how it differs from others, but intuitively I felt that it had to do with a life of discovering new things and constantly learning. I have been privileged to be a professor at MIT, one of the finest universities in the world, since my early twenties. In a typical day of my life, I meet with my doctoral students discussing ideas about making new discoveries, constantly learning new things. Every day is exciting as I meet with young people I love and respect trying to understand the world and making it better. I feel that I have found something that I love to do that makes my life meaningful. I would like to quote Steve Jobs, in his graduation speech he gave at Stanford in 2005:

“Your work is going to fill a large part of your life, and the only way to be truly satisfied is to do what you believe is great work. And the only way to do great work is to love what you do. If you haven't found it yet, keep looking. Don't settle. As with all matters of the heart, you'll know when you find it.”

I have always wished some things for myself:

  1. to do what I love.
  2. to continue to have high aspirations.
  3. to believe in myself, and
  4. to approach life in a positive way.

I wish the same things for you: to find what you love to do, to have high aspirations, to believe in yourselves and to keep a positive outlook in life.

Research
Robust Optimization

The goal of this work is to propose a tractable theory for optimization under uncertainty.

The first motivation for robust optimization is data uncertainty for structured mathematical programming problems. Under this perspective, we investigate different choices of uncertainty sets to model data uncertainty and characterize the structure of the resulting robust counterparts. We particularly focus on uncertainty sets for which the robust problem inherits the computational complexity of the underlying deterministic problem. Examples of concrete results in this direction include: (a) the robust counterpart of a linear programming problem (LP) is still an LP and of a mixed integer programming problem (MIP) is still a MIP of comparable size. (b) The robust counterpart of a polynomially solvable $0-1$ discrete optimization problem remains polynomially solvable. In particular, robust matching, spanning tree, shortest path, matroid intersection, etc. are polynomially solvable. (c) Robust network flows can also be solved as a polynomial number of modified network flow problems. (d) The robust counterpart of an $NP$-hard $\alpha$-approximable $0-1$ discrete optimization problem, remains $\alpha$-approximable. (e) Robust conic optimization problems retain their original structure. Specifically, robust second order cone problems (SOCPs) remain SCOPs and robust semidefinite optimization problems (SDPs) remain SDPs.

The second motivation of robust optimization is to model stochastic and dynamic optimization problems using uncertainty sets as opposed to probability distributions. Unlike dynamic and stochastic programming this robust approach does not suffer from the curse of dimensionality. As a test case, we apply this perspective to classical supply chain optimization problems under uncertainty, and show (a) the proposed approach is computationally tractable for high dimensions and in many cases leads to stronger solutions, (b) the optimal robust policies have the same structure as optimal policies obtained via dynamic programming; moreover, the robust approach is capable of characterizing the structure of the optimal policy even in cases where the structure of the optimal policy obtained via dynamic programming is unknown.

Current work has focused on constructing uncertainty sets from data, solving multistage adaptive optimization problems, as well as a great variety of applications in energy, operations management, finance and health care.

Health Care Analytics

In this work we aspire to develop methods for personalized medicine using a variety of analytics tools. So far, we have developed methods to a) personalized diabetes management and b) design of clinical trials for cancer. Current work focuses on a variety of other diseases.
We  have developed a system to make personalized lifestyle and health decisions for diabetes management, as well as for general health and diet management. In particular, we address the following components of the system: (a) efficiently learning preferences through a dynamic questionnaire that accounts for human behavior; (b) modeling blood glucose behavior and updating these models to match individual measurements; and (c) using the learned preferences and blood glucose models to generate an overall diet and exercise plan using mixed-integer robust optimization. We have implemented our system as an online application called LIA (Lifestyle Analytics).

We  have also developed a system  for the analysis and design of clinical trials that provides insights into what is the best currently available drug combination to treat a particular form of cancer and how to design new clinical trials that can discover improved drug combinations.  We developed semi-automated extraction techniques to build a comprehensive database of data from clinical trials. We use this database to develop statistical models from earlier trials that are capable of predicting the efficacy and toxicity of the combination of the drugs used, when the drugs used have been seen in earlier trials, but in different combinations. Then, using these statistical models, we developed optimization models that select novel treatment regimens that could be tested in clinical trials, based on the totality of data available on existing combinations. We have presented our work in the context of   gastric cancer, one of the leading causes of cancer death worldwide. Ultimately, our approach offers promise for improving life expectancy and quality of life for cancer patients at low cost.

Tractable stochastic analysis in high dimensions via a modern optimization lens

Modern probability theory, whose foundation is based on the axioms set forth by Kolmogorov, is currently the major tool for performance analysis in stochastic systems. While it offers insights in understanding such systems, probability theory is really not a computationally tractable theory in high dimensions. Correspondingly, some of its major areas of application remain unsolved when the underlying systems become multidimensional: Queueing networks, network information theory, pricing multi-dimensional financial contracts, auction design in multi-item, multi-bidder auctions among others.

We have proposed a new approach to analyze stochastic systems based on robust optimization. The key idea is to replace the Kolmogorov axioms as primitives of probability theory, with some   of the asymptotic implications of probability theory: the central limit theorem and law of large numbers and to define appropriate robust optimization problems to perform performance analysis. In this way, the performance analysis questions become highly structured optimization problems (linear, conic, mixed integer) for which there exist efficient, practical algorithms that are capable of solving truly large scale systems.

We have demonstrated that  the proposed approach achieves computationally tractable methods for  (a) analyzing queueing systems in the transient domain and queueing networks in the steady-state domain, (b)  characterizing the capacity region of network information theory and associated coding and decoding methods generalizing the work of Shannon, (c) pricing multi-dimensional  financial contracts generalizing the work of Black, Scholes and Merton, (d)  designing multi-item, multi-bidder auctions generalizing the work of Myerson.

Our overall objective is to develop an alternative to the classical theory of probability for performance analysis of stochastic systems that scales with dimension.

Multivariate statistics under a modern optimization lens

Key problems of classification and regression can naturally be written as optimization problems. While continuous optimization approaches has had a significant impact in statistics, discrete optimization has played a very limited role, primarily based on the belief that mixed integer optimization models are computationally intractable.  While such beliefs were accurate two decades ago, the field of discrete optimization has made very substantial progress.
 
We apply modern first order optimization methods to find feasible solutions for classical problems in statistics, and mixed integer optimization to improve the solutions and to prove optimality by finding matching lower bounds.

Specifically, we report results for the classical variable selection problem in regression currently solved by LASSO heuristically, least quantile regression, factor analysis.  Furthermore, we present an approach to build regression models based on mixed integer optimization. In all cases we demonstrate that the solutions found by modern optimization methods outperform the classical approaches. Most importantly, this body of work suggests that the   belief widely held in statistics that mixed integer optimization is not practically relevant for statistics applications needs to be revisited.

Our objective is develop the theory of statistics under a modern optimization lens. We will be offering a new doctoral level class in the spring of 2016 that revisits the major statistical problems under this lens.

PAPERS

Air Transportation

  1. The multi-airport ground-holding problem in air traffic control, (with A. Odoni and P. Vranas), Operations Research, 42, 2, 249-261, 1994.
  2. Dynamic ground-holding policies for a network of airports, (with A. Odoni and P. Vranas), Transportation Science, 28, 4, 275-291, 1994.
  3. Computational approaches to stochastic vehicle routing problems, (with P. Chervi and M. Peterson), Transportation Science, 29, 4, 342-352, 1995.
  4. Decomposition algorithms for analyzing transient phenomena in multi-class queuing networks in air transportation, (with A. Odoni and M. Peterson), Operations Research, 43, 6, 995-1011, 1995.
  5. Models and Algorithms for Transient Queuing Congestion at Airports, (with A. Odoni and M. Peterson), Management Science, 41, 1279-1295, 1995.
  6. The air traffic flow management problem with enroute capacities, (with S. Stock-Paterson), Operations Research, 46, 3, 406-422, 1998.
  7. The traffic flow management rerouting problem in air traffic control: a dynamic network flow approach, (with S. Stock-Paterson), Transportation Science, 34, 239-255, 2000.
  8. The Air Traffic Flow Management Problem: An Integer Optimization Approach, (with G. Lulli and A. Odoni), IPCO, 34-46, 2008.
  9. Optimal Selection of Airport Runway Configurations, (with M. Frankovitch and A. Odoni), Operations Research, 59, 1407–1419, 2011.
  10. Equitable and Efficient Coordination in Air traffic Flow Management, (with C. Barnhart, C. Caramanis, D. Fearing), submitted to Transportation Science, 2009.
  11. A Proposal for Network Air Traffic Flow Management Incorporating Fairness and Airline Collaboration, (with S. Gupta), submitted to Operations Research, 2010.

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Analytics

  1. Tenure Analytics: Models for Predicting Research Impact, (with E. Brynjolfsson, S. Reichman, J. Silberholz), Operations Research 63(6):1246-1261.

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Applied Probability

  1. An asymptotic determination of the minimum spanning tree and minimum matching constants in geometrical probability, (with G. van Ryzin), Operations Research Letters, 9, 223-231, 1990.
  2. Probabilistic analysis of the Held and Karp lower bound for the Euclidean traveling salesman problem, (with M. Goemans), Mathematics of Operations Research, 1, 72-89, 1991.
  3. The minimum spanning tree constant in geometrical probability and under the independent model; a unified approach, (with F. Avram), Annals of Applied Probability, vol. 2 ,1, 113-130, 1992.
  4. On central limit theorems in geometrical probability, (with F. Avram), Annals of Applied Probability, vol. 3, 4, 1033-1046, 1993.

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Approximation Algorithms

  1. Worst case examples for the spacefilling curve heuristic for the Euclidean traveling salesman problem, (with M. Grigni), Operations Research Letters, 8, 241-244, 1989.
  2. Survivable networks, LP relaxations and the parsimonious property, (with M. Goemans), Mathematical Programming, 60, 145-166, 1993.
  3. Locating discretionary service facilities II: maximizing market size, minimizing inconvenience, (with O. Berman and R. Larson), Operations Research, 43, 4, 623-632, 1995.
  4. The parsimonious property of cut covering problems and its applications, (with C. Teo), Operations Research Letters, 21, 123-132, 1997.
  5. From valid inequalities to heuristics: a unified view of primal-dual approximation algorithms in covering problems, (with C. Teo), Operations Research, 46, 4, 503-514, 1998.
  6. Rounding algorithms for covering problems, (with R. Vohra), Mathematical Programming, 80, 63-89, 1998.
  7. Semidefinite relaxations, multivariate normal distributions, and order statistics, (with Y. Ye), Handbook of Combinatorial Optimization (Vol. 3), D.-Z. Du and P.M. Pardalos (Eds.) pp.1-19 ,Kluwer Academic Publishers, 1998.
  8. Analysis of LP relaxations for multiway and multicut problems, (with C. Teo and R. Vohra), Networks, 34, 2, 102-113, 1999.
  9. On dependent randomized rounding algorithms, (with C. Teo and R. Vohra), Operations Research Letters, 24, 3, 105-114, 1999.
  10. Improved Randomized Approximation Algorithms for Lot Sizing Problems, (with C. Teo), Proceedings of the Fifth Conference on Integer Programming and Combinatorial Optimization, 1996.

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Fairness and Resource Allocation

  1. The Price of Fairness, (with V. Farias, N. Trichakis), Operations Research, 59, 1, 17-31, 2011.
  2. Flexibility, Fairness and Efficiency in Kidney Transplantation, (with V. Farias and N. Trichakis), submitted to Operations Research, 2011.
  3. On the Efficiency-Fairness Trade-off, (with V. Farias and N. Trichakis), Management Science, 58, 12, 2234–2250, 2012.

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Finance

  1. Optimal control of execution costs, (with Andrew Lo), Journal of Financial Markets, 1, 1-50, 1998.
  2. Optimal control of execution costs for portfolios, (with Paul Hummel and Andrew Lo), Computing in Science and Engineering, 40-53, 1999.
  3. Portfolio construction through mixed integer programming, (with C. Darnell and R. Soucy), Interfaces, 29, 49-66, 1999.
  4. When is time continuous, (with Leonid Kogan and Andrew Lo), Journal of Financial Economics, 55, 173-204, 2000.
  5. Hedging Derivative Securities and Incomplete Markets: An e-Arbitrage Approach, (with Leonid Kogan and Andrew Lo), Operations Research, 49, 3, 372-397, 2001.
  6. On the relation between option and stock prices: a convex optimization approach, (with Ioana Popescu), Operations Research, 50, 2, 358-374, 2002.
  7. An Optimization Approach to Credit Risk, (with Dessi Pachamanova), December, 2002.
  8. Shortfall as a risk measure: properties and optimization, (with Geoffrey Lauprete and Alex Samarov), Journal of Economic Dynamics and Control, 28, 7, 1353-1381, 2004.
  9. No-arbitrage bounds on American put options with a single maturity, (with P. Shah),
    submitted to Operations Research, 2008.
  10. An Analysis of the Guaranteed Withdrawal Benefits for Life Option, (with P. Shah), submitted to Journal of Insurance, 2008.
  11. Inverse Optimization: A New Perspective on the Black-Litterman Model, (with V.Gupta and I. Paschalidis), Operations Research, 60, 6, 1389–1403, 2012.

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Health Care

  1. Algorithmic Prediction of Health-Care Costs, (with M. Bjarnadottir, M. Kane, C. Kryder, R. Pandey. S. Vempala and G. Wang), Operations Research, Vol. 56, No. 6, 1382-1392, 2008.
  2. A hybrid approach to beam angle optimization in intensity-modulated radiation therapy, (with V. Cacchiani ,D. Craft, O. Nohadani), submitted to Computers and Operations Research, 2012.
  3. Measuring Quality in Diabetes Care: An Expert-based Statistical Approach, (with D. Czerwinski and M. Kane), 2013.
  4. An Analytics Approach to Designing Combination Chemotherapy Regimens for Cancer, (with A. O'Hair, S. Relyea and J. Silberholz), Management Science, 2016.
  5. Personalized Diabetes Management Using Electronic Medical Records, (with N. Kallus, A. Weinstein, and Y. Zhuo), Diabetes Care, 40, 210–217, 2017.

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Large Deviations

  1. On the large deviation behavior in acyclic networks of G/G/1 queues, (with I. Paschalidis and J. Tsitsiklis), Annals of Applied Probability, 8, 4, 1027-1069, 1998.
  2. Asymptotic buffer overflow probabilities in multiclass multiplexers, (with I. Paschalidis and J. Tsitsiklis), IEEE Automatic Control, 43, 3, 315-335, 1998.
  3. Large deviation analysis of the generalized processor sharing policy, (with I. Paschalidis and J. Tsitsiklis), Queuing Systems and their Applications, 32, 319-349, 1999.
  4. Deducing queuing from transactional data: the queue inference engine, revisited,(with L. Servi), Operations Research, 40, S217-S228, 1992.

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Machine Learning under a Modern Optimization Lens

  1. Estimation of time-varying parameters in statistical models: an optimization approach, (with D. Gamarnik and J. Tsitsiklis), Machine Learning, 35, 3, 225-245, 1999.
  2. Classification and Regression via Integer Optimization, (with Romy Shioda), Operations Research, 55, 252-271, 2007.
  3. An Integer Optimization Approach to Associative Classification, (with A. Chang and C. Rudin), 26th Annual Conference on Neural Information Processing Systems, 3302-3310, 2012.
  4. Characterization of the equivalence of robustification and regularization in linear, median, and matrix regression, (with M. Copenhaver), 2014.
  5. The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples, (with M. Johnson and N. Kallus), Operations Research, Vol. 63, No. 4, July–August 2015, pp. 868–876.
  6. An Algorithmic Approach to Linear Regression, (with A. King), submitted to Operations Research.
  7. Best Subset Selection via a Modern Optimization Lens, (with A. King and R. Mazumder), to appear in Annals of Statistics, 2016.
  8. Inventory Management in the Era of Big Data, (with N. Kallus and A. Hussain), Production and Operations Management, 25, 12, 2006--2009, 2016.
  9. Optimal classification trees, (with J. Dunn), Machine Learning, April 2017.
  10. Certifiably Optimal Low Rank Factor Analysis, (with M. Copenhaver and R. Mazumder), Journal of Machine Learning Research, 18, 1-53, 2017.
  11. The Trimmed Lasso: Sparsity and Robustness, (with M. Copenhaver and R. Mazumder), submitted to IEEE Transactions on Information Theory.
  12. Logistic Regression: From Art to Science, (with A. King), Statistical Science, Vol. 32, No. 3, 367–384, 2017.
  13. From Predictive Methods to Missing Data Imputation: An Optimization Approach, (with C. Pawlowski and Y. Zhuo), submitted to Journal of Machine Learning Research 18 (2018) 1-39.
  14. Robust Classification, (with J. Dunn, C. Pawlowski, and Y. Zhuo), INFORMS Journal on Optimization, Vol. 1, No. 1, Winter 2019, pp. 2–34, 2018.

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Moment problems

  1. Probabilistic Combinatorial Optimization: Moments, Semidefinite Programming and Asymptotic Bounds, (with Karthik Natarajan, Chung Piaw Teo), SIAM Journal of Optimization, 15, 1, 185–209, 2004.
  2. Optimal mean-variance bounds on the expectation of the highest order statistics, (with Karthik Natarajan, Chung Piaw Teo), May, 2004.
  3. Persistence in Discrete Optimization under Data Uncertainty, (with Karthik Natarajan, Chung Piaw Teo), Mathematical Programming Series B, 108, 251–274, 2006.
  4. Bounds on Linear PDEs via Semidefinite Optimization, (with Constantine Caramanis), Mathematical Programming Series A & B, 108, 135-158, 2006.
  5. Optimal inequalities in probability theory: A convex optimization approach, (with Ioana Popescu), SIAM Journal of Optimization, 15, 3, 780-804, 2004.
  6. Moment problems and semidefinite programming, (with Ioana Popescu and Jay Sethuraman), in Handbook on Semidefinite Programming: Theory, Algorithms, and Applications, H. Wolkovitz, ed., 469--509, 2000.
  7. Tight bounds on expected order statistics, (with K. Natarajan and C. Teo), Probability in Engineering and Information Systems, 20, 4, 667-686, 2006.
  8. A semidefinite optimization approach to the steady-state analysis of queueing systems, (with K. Natarajan), Queuing Systems and Applications, 56, 1, 27-40, 2007.
  9. Bounds on Some Contingent Claims with Non-Convex Payoff Based on Multiple Assets, (with X. V. Doan and K. Natarajan), Technical Report, Operations Research Center, MIT, August 2007.
  10. Approximating integrals of multivariate exponentials: A moment approach, (with X. Vinh Doan and J. Lasserre), Operations Research Letters, 36, 2, 205-210, 2008.
  11. Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion, (with X. V. Doan, K. Natarajan and C. P. Teo), submitted to Mathematics of Operations Research, April 2008.

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Operations Management

  1. Probabilistic service level guarantees in make-to-stock manufacturing system, (with I. Paschalidis), Operations Research, 49, 1, 119-133, 2001.
  2. Multistage Lot Sizing Problems via Randomized Rounding, (with C. Teo), Operations Research, 49, 4, 599-608, 2001.

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Optimization

  1. Simulated annealing, (with J. Tsitsiklis), Statistical Science, Vol.8, No. 1, 10-15, 1993.
  2. A technique for speeding up the solution of the Lagrangean dual, (with J. Orlin), Mathematical Programming, vol. 63, 1, 23-46, 1994.
  3. On the worst case complexity of potential reduction algorithms for linear programming, (with X. Luo), Mathematical Programming. 77, 321-333, 1997.
  4. A new algebraic geometry algorithm for integer programming, (with G. Perakis and S. Tayur), Management Science, 46, 999-1008, 2000.
  5. Solving convex programs by random walks, (with Santosh Vempala), Journal of the ACM, 51, 4, 540-556, 2004.
  6. Solving Asymmetric Variational Inequalities via Convex Optimization, (with M. Aghassi and G. Perakis), Operations Research Letters, 481-490, 2006.
  7. Algorithm For Cardinality-Constrained Quadratic Optimization, (with R. Shioda), to appear in Computational Optimization and Applications, 2007.
  8. "A general purpose local search algorithm for binary optimization", (with D. Iancu, D. Katz), submitted to INFORMS Journal of Computing, 2008.
  9. "An accelerated first-order method for solving unconstrained polynomial optimization problems", (with R. Freund, A. Sun), submitted to Optimization Methods and Software, 2011.
  10. "Data-driven estimation in equilibrium using inverse optimization", (with V. Gupta, I. Paschalidis), Mathematical Programming, Series A, 2014.
  11. "Optimizing over coherent risk measures and non-convexities: a robust mixed integer optimization approach", (with A. Takeda), Computational Optimization and Applications, 62, 613–639, 2015.
  12. "Learning Preferences Under Noise and Loss Aversion: An Optimization Approach", (with A. O'Hair), Operations Research, 61(5):1190-1199, 2013.
  13. Optimizing schools’ start time and bus routes, (with A. Delarue and S. Martin), PNAS, 2019.

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Queuing Theory

  1. On the exact steady state solution of the Ek/C2/s queue, (with X. Papaconstantinou), European Journal of Operations Research, 37(2), 272-287, 1988.
  2. On the steady-state solution of the M/C2(a,b)/s queuing system, (with X. Papaconstantinou), Transportation Science, 22, 2, 125-138, 1988.
  3. An exact FCFS waiting time analysis for a general class of G/G/s queuing systems, Queuing Systems Theory and Applications, 3, 305-320, 1988.
  4. Relations between the pre-arrival and post-departures state probabilities and the FCFS waiting-time distribution for the Ek/G/s queue, (with X. Papaconstantinou), Naval Research Logistics Quarterly, 37, 135-149, 1990.
  5. An analytic approach to a general class of G/G/s queuing systems, Operations Research, 38, 1, 139-155, 1990.
  6. Transient and busy period analysis of the GI/G/1 queue as a Hilbert factorization problem, (with J. Keilson, D. Nakazato, H. Zhang), Journal of Applied Probability, 28, 873-885, 1991.
  7. Transient and busy period analysis for the GI/G/1 queue; The method of stages, (with D. Nakazato), Queuing Systems and Applications, 10, 153-184, 1992.
  8. The distributional Little's law and its applications, (with D.Nakazato), Operations Research, 43, 2, 298-310, 1995.
  9. A unified method to analyze overtake free systems, (with G. Mourtzinou), Advances in Applied Probability, 28, 588-625, 1996.
  10. Multiclass queuing systems in heavy traffic: an asymptotic approach based on distributional and conservation laws, (with G. Mourtzinou), Operations Research, 45, 3, 470-487, 1997.
  11. Transient distributional laws and their applications, (with G. Mourtzinou), Queuing Systems and their Applications, 25, 115-155, 1997.
  12. Decomposition results for general polling systems and their applications, (with G. Mourtzinou), Queuing Systems and their Applications, 31, 295-316, 1999.

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Revenue Management

  1. Simulation-Based Booking Limits for Airline Revenue Management, (with Sanne de Boer), Operations Research, 53, 1, 2005.
  2. Joint network pricing and resource allocation, (with Sanne de Boer), March, 2004.
  3. Revenue Management in a Dynamic Network Environment, (with Ioana Popescu), Transportation Science, 37, 257-277, 2003.
  4. Dynamic Pricing; A Learning Approach, (with Georgia Perakis), Models for Congestion Charging/Network Pricing, 2005.
  5. Restaurant Revenue Management, (with Romy Shioda), Operations Research, 51, 3, 472--486, 2003.
  6. A Learning Approach to Customized Marketing, (with Adam Mersereau), December, 2003.
  7. Optimal Bidding in Online Auctions, (with Jeff Hawkins and Georgia Perakis), to appear in Pricing and Revenue Management, December, 2002.
  8. Simulation Based Booking Limits for Airline Revenue Management, (with S. de Boer), Operations Research, 53, 1, 90-106, 2005.
  9. Dynamic pricing and inventory control for multiple products, (with S. de Boer), Journal of Revenue Management, 17, 303-319, 2005.
  10. A learning Approach for Interactive Marketing to A Customer Segment, (with A. Mersereau), Operations Research, 55, 6, 1120-1135, 2007.

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Robust Optimization

  1. Tractable Approximations to Robust Conic Optimization Problems, (with Melvyn Sim), Mathematical Programming, 107(1), 5-36, 2006.
  2. Robust Discrete Optimization under Ellipsoidal Uncertainty Sets, (with Melvyn Sim), April 2004.
  3. Robust Linear Optimization under General Norms, (with Dessi Pachamanova and
    Melvyn Sim), Operations Research Letters, 32, 510-516, 2004.
  4. A Robust Optimization Approach to Inventory Theory, (with Aurelie Thiele), Operations Research, 54, 1, 150-168, 2006.
  5. The price of Robustness, (with Melvyn Sim), Operations Research, 52, 1, 35-53, 2004.
  6. Robust Discrete optimization and Network Flows, (with Melvyn Sim),
    Mathematical Programming Series B, 98:49-71, 2003.
  7. Robust Game Theory, (with M. Aghassi), Mathematical Programming, 107, 231-273, 2006.
  8. Robust and data-driven optimization: modern decision making under uncertainty, (with A. Thiele), Tutorials on Operations Research, INFORMS, Chapter 4, 195-122, 2006.
  9. Constrained Stochastic LQC: A Tractable Approach, (with D. Brown), IEEE Journal of Automatic Control, 52, 10, 1826-1841, 2007.
  10. Robust Optimization in Electromagnetic Scattering Problems, (with O. Nohadani and K. M. Teo), Journal Applied Physics, 101, 7, 074507, 2007.
  11. Robust Multiperiod Portfolio Management in the Presence of Transaction Costs, (with D. Pachamanova), Computers and Operations Research, 35, 1, 3-17, 2008.
  12. Constructing uncertainty sets for robust linear optimization, (with D. Brown), to appear in Operations Research.
  13. Finite adaptability in linear optimization, (with C. Caramanis), to appear in IEEE Transactions in Automatic Control.
  14. Robust nonconvex optimization for simulation based problems, (with O. Nohadani and K. M. Teo), to appear in Operations Research.
  15. Robust chirped mirrors, (with J. Birge, O. Nohadani and F. Kartner), Applied Optics, 47, 14, 2630-2636, 2008.
  16. Data-Driven and Robust Optimization Approaches to Call Centers, (with X. V. Doan), revised and resubmitted to Manufacturing & Service Operations Management, November 2008.
  17. On the Power of Robust Solutions in Two-Stage Stochastic and Adaptive Optimization Problems, (with Vineet Goyal), submitted to Mathematics of Operations Research, 2009.
  18. A soft robust model for optimization under ambiguity, (with Aharon Ben-Tal and David B. Brown), September 2009.
  19. Nonconvex Robust Optimization for Problems with Constraints, (with Omid Nohadani and Kwong Meng Teo), INFORMS Journal on Computing (preprint), 2009.
  20. Robust optimization with simulated annealing, (with Omid Nohadani), Journal of Global Optimization, 2009.
  21. Optimality of Affine Policies in Multistage Robust Optimization, (with Dan A. Iancu and Pablo A. Parrilo), Mathematics of Operations Research, May 2010.
  22. Performance analyis of queueing networks via robust optimization, (with D. Gamarnik and A. Rikun), to appear in Operations Research.
  23. Theory and applications of robust optimization, (with D. Brown and C. Caramanis), to
    appear in SIAM Review.
  24. A hierarchy of policies for adaptive optimization, (with D. Iancu and P. Parrilo), to appear in IEEE Automatic Control.
  25. A Geometric Characterization of the Power of Finite Adaptability in Multi-stage Stochastic and Adaptive Optimization, (with V. Goyal and A. Sun), to appear in Mathematics of
    Operations Research
    .
  26. On the Power and Limitations of Affine Policies in Two-Stage Adaptive Optimization, (with V. Goyal), to appear in Mathematical Programming.
  27. Robust Logistic Regression, (with A. Fertis), submitted to Operations Research, 2008.
  28. On the Equivalence of Robust Optimization and Regularization in Statistics, (with A.
    Fertis), submitted to Operations Research, 2009.
  29. An Adaptive Local Search Algorithm for Solving Mixed Integer Optimization Problems,
    (with V. Goyal), submitted to Mathematical Programming, 2009.
  30. Robust Option Pricing (with C. Bandi), European Journal of Operations Research, 238, 842-853, 2014.
  31. On the Power of Robust Solutions in Nonlinear Adjustable Optimization Problems, (with
    V. Goyal), submitted to Operations Research, 2011.
  32. Adaptive Robust Optimization for the Security Constrained Unit Commitment Problem, (with E. Litvinov, A. Sun, J. Zhao, and T. Zheng), IEEE Transactions on Power Systems, 28, 1, 52-63, 2013.
  33. Tractable Stochastic Analysis in High Dimensions via Robust Optimization, (with C. Bandi), Mathematical Programming, 134, 1, 23-70, 2012.
  34. On the Performance of Affine Policies for Two-Stage Adaptive Optimization: a Geometric Perspective, (with H. Bidkhori), Mathematical Programming, Series A, 2013.
  35. Multistage Robust Mixed Integer Optimization with Adaptive Partitions, (with I. Dunning), Submitted to Operations Research, 2014.
  36. Data-driven learning in dynamic pricing using adaptive optimization, (with P. Vayanos), Submitted to Operations Research, 2014.
  37. Robust Queueing Theory, (with C. Bandi and N. Youssef), Submitted to Operations Research, 2014.
  38. Robust Transient Multi-Server Queues and Feedforward Networks, (with C. Bandi and N. Youssef), Submitted to Operations Research, 2014.
  39. Robust Fluid Processing Networks, (with E. Nasrabadi and I. Paschalidis), IEEE Transactions on Automatic Control, Vol. 60, NO. 3, MARCH 2015.
  40. Duality in Two-Stage Adaptive Linear Optimization: Faster Computation and Stronger Bounds, (with F. de Ruiter), INFORMS Journal on Computing, Vol. 28, No. 3, pp. 500–511, Summer 2016.
  41. Data-driven robust optimization, (with V. Gupta and N. Kallus), Mathematical Programming, Series A, DOI 10.1007/s10107-017-1125-8, February, 2017.
  42. Robust Sample Average Approximation, (with V. Gupta and N. Kallus), Mathematical Programming, Series A, DOI 10.1007/s10107-017-1174-z, June, 2017.
  43. Robust transient analysis of multi-server queueing systems and feed-forward networks, (with C. Bandi and N. Youssef), Queueing Systems, pp 1–63, January 2018.
  44. Binary decision rules for multistage adaptive mixed-integer optimization, Mathematical Programming, pp 395–433, February 2018.

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Stochastic Networks

  1. Optimization of multiclass queuing networks: polyhedral and nonlinear characterizations of achievable performance, (with I. Paschalidis and J. Tsitsiklis), Annals of Applied Probability, 4, 1, 43-75, 1994.
  2. Optimization of multiclass queuing networks:a linear control approach, (with F. Avram and M. Ricard), Stochastic networks; proceedings of the IMA,(F. Kelly and R. Williams, editors), 199-234, 1995.
  3. Stability conditions for multiclass fluid networks, (with D. Gamarnik and J. Tsitsiklis), IEEE Automatic Control, 41, 1618-1631, 1996.
  4. A new algorithm for state-constrained separated continuous linear programs, (with X. Luo), SIAM Journal on Control and Optimization, 37, 1, 177-210, 1998.
  5. Bounds and policies for loss networks, (with T. Chryssikou), Operations Research, 47, 3, 379-394, 1999.
  6. Asymptotically optimal algorithms for job shop scheduling and packet routing, (with D. Gamarnik), Journal of Algorithms, 33, 296-318, 1999.
  7. An Approximate Dynamic Programming Approach to Multi-dimensional Knapsack Problems, (with Ramazan Demir), Management Science, 48, 4, 550--565, 2002.
  8. From fluid relaxations to practical algorithms for job shop scheduling: the holding cost objective, (with David Gamarnik and Jay Sethuraman), Operations Research, 51, 5, 798--813, 2003.
  9. From fluid relaxations to practical algorithms for job shop scheduling: the makespan objective, (with Jay Sethuraman), Mathematical Programming, 92, 1, 61--102, 2002.
  10. Performance of Multiclass Markovian Queueing Networks Via Piecewise Linear Lyapunov Functions, (with David Gamarnik and John Tsitsiklis), Annals of Applied Probability, 11, 4, 1384-1428, 2001.
  11. Dynamic Classification of Online Customers, (with A. Mersereau and N. Patel), 3rd SIAM Conference in Data Mining, 107-118, 2003.

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Stochastic Scheduling

  1. Branching bandits and Klimov's problem: achievable region and side constraints, (with I. Paschalidis and J. Tsitsiklis), IEEE Automatic Control, 40, 12, 2063-2075, 1995.
  2. The achievable region method in the optimal control of queuing systems; formulations, bounds and policies, Queuing Systems and Applications, 21, 3-4,337-389, 1995.
  3. Conservation Laws, Extended Polymatroids and Multiarmed Bandit Problems; a Polyhedral Approach to Indexable Systems, (with Jose Niño-Mora), Mathematics of Operations Research, 21, 2, 257-306, 1996.
  4. Optimization of multiclass queuing networks with changeover times via the achievable region approach: Part I, the single-station case, (with J. Niño-Mora), Mathematics of Operations Research, 24, 2, 306-329, 1999.
  5. Optimization of multiclass queuing networks with changeover times via the achievable region approach: Part II, the multi-station case, (with J. Niño-Mora), Mathematics of Operations Research, 24, 2, 331-361, 1999.
  6. Restless bandits, linear programming relaxations and a primal-dual heuristic, (with J. Niño-Mora), Operations Research, 48, 80-90, 2000.
  7. The Generalized Restless Bandit Problem: Algorithms and Applications, (with A. Becker
    and Xuan Vinh Doan), submitted to Operations Research, 2011.

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Vehicle Routing

  1. On probabilistic traveling salesman facility location problems, Transportation Science, 3, 184-191, 1989.
  2. The probabilistic minimum spanning tree problem, Networks, 20, 245-275, 1990.
  3. A priori optimization, (with P. Jaillet and A. Odoni), Operations Research, 38, 6, 1019-1033, 1990.
  4. A stochastic and dynamic vehicle routing problem in the Euclidean plane, (with G. van Ryzin), Operations Research, 39, 4, 601-615, 1991.
  5. A vehicle routing problem with stochastic demand, Operations Research, 40, 574-585, 1992.
  6. Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles, (with G. van Ryzin), Operations Research, 41, 60-76, 1993.
  7. Further results on the probabilistic traveling salesman problem, (with L. Howell), European Journal of Operations Research, 65, 1, 68-95, 1993.
  8. Stochastic and dynamic vehicle routing with general arrival and demand distributions, (with G. van Ryzin), Advances in Applied Probability, 25, 4, 947-978, 1993.
  9. A new generation of vehicle routing research, (with D. Simchi-Levi), Operations Research, 44, 2, 286-304, 1996.

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Earlier Papers

  1. Approximate Dynamic Programming Algorithms for Facility Location Problems, (with C. Teo and R. Vohra), submitted to INFORMS Journal of Computing
  2. A Linear Optimization Approach to the Lov\'asz Local Lemma,(with E. Perevalov), submitted to Mathematical Programming
  3. Constructing cutting plane algorithms for integer programming: a geometric approach, (with R. Weismantel), submitted to Mathematical Programming
  4. A duality theory for 0/1 integer programming, (with R. Weismantel),submitted to Mathematics of Operations Research

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Books
MACHINE LEARNING UNDER A MODERN OPTIMIZATION LENS

Co-author: Jack Dunn
Dynamic Ideas, Belmont, Massachusetts, 2019.

The book provides an original treatment of machine learning (ML) using convex, robust and mixed integer optimization that leads to solutions to central ML problems at large scale that can be found in seconds/minutes, can be certified to be optimal in minutes/hours, and outperform classical heuristic approaches in out-of-sample experiments.

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THE ANALYTICS EDGE

Co-authors: Allison K. O'Hair and William R. Pulleyblank
Dynamic Ideas, Belmont, Massachusetts, 2016.

The Analytics Edge provides a unified, insightful, modern and entertaining treatment of analytics. The book covers the science of using data to build models, improve decisions, and ultimately add value to institutions and individuals. Most of the chapters start with a real world problem and data set, then describe how analytics has provided an edge in addressing that particular problem.

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Introduction to Linear Optimization

Co-author: John Tsitsiklis
Dynamic Ideas, Belmont, Massachusetts, 2008.

The book is a modern and unified introduction to linear optimization (linear programming, network flows and integer programming) at the PhD level. It covers, in addition to the classical material, all the recent developments in the field in the last ten years including the development of interior points, large scale optimization models and algorithms and complexity of linear optimization. It emphasizes the underlying geometry, intuition and applications of large scale systems.

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Data, Models and Decisions
The Fundamentals of Management Science, 2nd Edition

Co-author: Robert Freund
Dynamic Ideas, Belmont, Massachusetts, 2004.

This book represents a departure from existing textbooks. Rather than covering methodology, the book introduces decision support systems through real world applications, and uses spreadsheets to model and solve problems. It uses management science techniques (statistics, simulation, probabilistic modeling and optimization), but only as tools to facilitate problem solving.

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Optimization over Intergers

Co-author: Robert Weismantel
Dynamic Ideas, Belmont, Massachusetts, 2005.

The purpose of this book is to provide a unified, insightful, and modern treatment of the theory of integer optimization with an eye towards the future. We have selected those topics that we feel have influenced the current state of the art and most importantly we feel will affect the future of the field. We depart from earlier treatments of integer optimization by placing significant emphasis on strong formulations, duality, algebra and most importantly geometry.

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TEACHING
Established at MIT, Professor Bertsimas has taught an array of classes within his field.

Classes taught in the past include:

  • 15.071 - The Analytical Edge
  • 15.081J - Introduction to Mathematical Programming
  • 15.083J - Combinatorial Optimization
  • 15.072 - Queues: Theory and Applications
  • 15.098 - SPECIAL SEMINAR IN APPLIED PROBABILITY
  • 15.060 - Data, Models and Decisions
  • 15.45s - Finance Made Dificult
  • 15.093J - Optimization Methods
  • 15.095 - Machine Learning Under a Modern Optimization Lens
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