Author Spotlight

In Conversation With...
Aharon Ben-Tal

When trying to solve complex, real-world problems in which the data are uncertain, the field of robust optimization plays a significant role in determining the optimal outcome. Conceived and developed extensively by Aharon Ben-Tal, Arkadi Nemirovski, and Laurent El Ghaoui in the 1990s, robust optimization (RO) addresses “optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution” [1]. The applicability of RO to daily life is widespread, yet unrealized by the lay public. From applications in medical imaging to civil and structural engineering, RO helps resolve many intractable, everyday problems.

Aharon Ben-Tal has been a visionary leader in optimization in general and in RO in particular. He and Nemirovski authored the seminal paper “Robust convex optimization" which appeared in Mathematics of Operations Research in 1998 [2]. This paper laid the foundation of RO and was the first in a long series of publications resulting in the creation of this new area of optimization.

For his remarkable lifetime achievements in the area of optimization, he was awarded the INFORMS Optimization Society’s Khachiyan Prize in 2016. When bestowing the Khachiyan Prize, the selection committee reserved special praise for Ben-Tal’s groundbreaking theories in RO: “…it may be argued that the scholarly achievement with the greatest impact has been his path-breaking research on robust optimization” [3].

Over the decades, Aharon Ben-Tal has authored more than 130 papers (which have to date received more than 19,000 citations), received 14 significant awards, and served on editorial boards for 10 journals (including Mathematics of Operations Research, Management Science, and Operations Research). One of Ben-Tal’s former graduate students, Marc Teboulle (a current Area Editor for MOR), described the unique characteristics of Ben-Tal’s research as “[the ability to identify] the ‘right’ problems and questions, the clarity of exposition, the mathematical elegance, the depth and breadth, and above all, originality.”

INFORMS interviewed Aharon Ben-Tal in spring 2017 to see what fuels his intellectual fire these days, ask about his predictions for the future of operations research (OR), and garner some advice for students entering the field. What follows is the third in a series of interviews that showcase the thought-leaders in the field of operations research.

INFORMS: Your seminal paper in Mathematics of Operations Research (MOR), “Robust convex optimization” [2], is one of the highest cited papers ever published in the journal, with 1,995 citations since it was published in 1998. What, in your opinion, are the most visible and important real-world application(s) in which robust convex optimization has had an enduring impact?

BEN-TAL: This is a difficult question…if you write in Google “applications of robust optimizations” you get more than 30,000,000 items! Some of the application areas that I consider important are: medical imaging, IMRT (intensive modulated radiation therapy), energy planning, design of mechanical structures, Integrated circuit design, supply chain management, finance (portfolio selection), and machine learning.

INFORMS: Can you tell us about how you and coauthor Arkadi Nemirovski came to collaborate on this paper?

BEN-TAL: Our collaboration started on problems in structural design; there, we encountered a case in which a small, unexpected force affecting a structure could cause it collapse. That led to a general question on how to avoid severe infeasibilities in case data are uncertain. Our answer to that question was given in the MOR paper.

INFORMS: You and Nemirovski have co-authored five published MOR articles to date. Are you and he still actively working together in your research? If so, what project(s) are you jointly working on at the moment?

BEN-TAL: Our last joint paper was the 2015 MOR paper, “On solving large-scale polynomial convex problems by randomized first-order algorithms” [4]. Since Nemirovski left Technion [Israel Institute of Technology], our collaboration has, unfortunately, diminished. We still have long Skype/telephone discussions on the future direction optimization research is taking (or should be taking…).

INFORMS: One of your former advisees, Marc Teboulle, who is a current Area Editor for MOR, described your impact on him as follows: “He stimulated me to work hard and excel in research from my very first steps by revealing to me the key aspects that a scholar’s work should encompass to be considered ‘top quality research.’” Could you share some of your tips for the early career researcher who is reading this article?

BEN-TAL: First, if offered a full faculty position right after receiving your PhD, don’t give into the temptation to take it. You’ll likely be better off trying to get a good postdoc position. This will make a more substantial contribution to your future career. Second, target top-rated journals right from the start when determining where to submit your research papers (“quality before quantity”). Third, diversify your research area beyond that of your PhD thesis. Fourth, try to enter an application area where you feel that you can make a contribution.

INFORMS: Teboulle also identified a key aspect of your success as, “identifying the ‘right’ problems and questions.” Could you give us an example where your input and calculations uncovered the real problem (as opposed to the ‘perceived’ problem) and helped shaped the questions that needed to be answered?

BEN-TAL: Robust optimization (RO) is just such an example! For an optimization problem under uncertainty, the real problem is to offer models for which the user can provide the data, and the optimizer can solve efficiently the resulting mathematical programming problem, including dynamical ones. RO methodology was aimed to address these challenges right from the start and is the reason why it is so widely adopted.

INFORMS: Thinking back on your early career, who was your mentor? Tell us a little bit about what role that person played in guiding your early career?

BEN-TAL: My thesis advisor, Adi Ben-Israel, was the one who guided my early career. He is credited with teaching me how to write rigorous yet clear papers. He offered me the freedom to pursue my research directions even when they were risky. We became eventually good friends and collaborated on many papers.

INFORMS: Do you have any suggestions for students who are searching for a mentor?

BEN-TAL: First, make sure he or she is still an active researcher who is internationally recognized. Find out what the mentor’s former students are doing after graduation; similarly, talk to his/her current students. But most important: ask yourself whether the research topics that the mentor suggests for your thesis really excite you.

INFORMS: What is the best advice you can give to students in your field?

BEN-TAL: Avoid working in a "crowded" area (e.g., first-order methods). Most likely, your

INFORMS: What about your career might surprise us?

BEN-TAL: Some of the ideas for my master’s thesis were conceived while I was under heavy artillery fire by the Egyptian army during the War of Attrition in the Suez Canal. Eventually, three papers were published based on these bombs…

INFORMS: You were the 2016 winner of the INFORMS Optimization Society’s Khachiyan Prize for outstanding lifetime contributions to the field of optimization. What do you consider to be your most significant lifetime accomplishment to date?

BEN-TAL: I will mention two such contributions: first, the derivation of a second-order optimality condition for constrained optimization problems with functions that are not even once differentiable. The 1982 paper “Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems” [5], jointly authored with Jochem Zowe, in which this theory was introduced, studies an abstract optimization problem (P) in infinite dimensional spaces. From a general extremality condition, a variety of necessary conditions of first and second order, with or without differentiability assumptions, are derived for special cases of the general one. Thirty-five years after its publication, the paper is still cited regularly.

Second, the development, with Arkadi Nemirovski, of RO theory, algorithms, and applications, for both static and dynamic problems. This theory created a new subarea of optimization and OR and enabled the solution of problems affected by uncertainty in a vast array of applications.

INFORMS: What recent project have you been involved in that you are most proud of?

BEN-TAL: Recently I've been working on optimization problems under distributional ambiguity: in other words, the data are stochastic but only partial information on its distribution is available. Quite unexpectedly, it turns out that progress was achieved by using results from my very first paper, “More bounds on the expectation of a convex function of a random variable" [6]!

INFORMS: If we were sitting here a year from now celebrating what a great year it's been for you, what would we be celebrating?

BEN-TAL: Being awarded the INFORMS Khachiyan Prize and the Life Achievement Award from the Operations Research Society of Israel.

INFORMS: Tell us something that not many people know about you.

BEN-TAL: I studied music (piano) and was mainly interested in composition. I still have not given up on this dream…

References

[1] Wikipedia. Robust optimization. Accessed June 28, 2017.
[2] Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math. Oper. Res. 23(4):769–805.
[3] INFORMS Optimization Society (2016) Aharon Ben-Tal is selected as the winner of the 2016 INFORMS Optimization Society Khachiyan Prize. Accessed June 28, 2017.
[4] Ben-Tal A, Nemirovski A (2015) On solving large-scale polynomial convex problems by randomized first-order algorithms. Math. Oper. Res. 40(2): 474–494.
[5] Ben-Tal A, Zowe J (1982) Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems. Math Program. 24(1):70–91.
[6] Ben-Tal A, Hochman E (1972) More bounds on the expectation of a convex function of a random variable. J. Appl. Probab. 9(4):803–812.

For comments or more information about this series, please contact the Managing Editor, Stephanie Dean.