We then apply the robust optimization methodology ben tal and nemirovski. Robust optimization ro isa modeling methodology, combined with computational tools, to pro. Arkadi nemirovski is professor of industrial and systems engineering at georgia institute of technology. Robust optimization methodology and applications springerlink. Ben tal and nemirovski 1998 are considered as the birth of this eld. Robust optimization with decisiondependent information. In contrast to ro, stochastic optimization starts by assuming the uncertainty has a probabilistic. Risk mitigation in humanitarian relief supply chains. This cited by count includes citations to the following articles in scholar. The model is given by a new methodology for optimization under uncertainty the robust counterpart approach. Milton stewart school of industrial and systems engineering at the georgia institute of technology. As shown in ben tal and nemirovski 2000, in many cases the robust objective value is only slightly higher than the version that neglects uncertainty. Michael poss introduction to robust optimization may 30, 2017 10 53.
Robust optimization ro is a relatively young methodology, developed mainly in the course of the last 15 years to analyze and optimize the performance of complex systems. Aharon ben tal arkadi nemirovski robust optimization methodology and applications received. Aharon ben tal is professor of operations research at the technion, israel institute for technology. Arkadi nemirovski and publisher princeton university press. Practical robust optimization an introduction lnmb. Algorithm engineering in robust optimization arxiv. Furthermore, as we will illustrate in 2, this problem is compounded by the fact that the deterministic forms of many robust optimization models are exceedingly complex and tedious to model explicitly. September 12, 2001 published online february 14, 2002 springerverlag 2002 abstract. In the paper, we develop, discuss and illustrate by simulated numerical results a new model of multistage asset allocation problem. Pdf robust optimization ro is a modeling methodology, combined with computational tools, to process.
Theorem ben tal and nemirovski 1998 problem uco is equivalent to a mixedinteger linear program. Robust optimization is a field of optimization theory that deals with 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 andor its solution. The data a,b associated with a linear program 1 min c t x ax. Partially supported by grant scho 114032 within the dfg programmealgorithm engineering and. Robust optimization ro is a modeling methodology, combined with computational tools, to process optimization problems in which the data are uncertain and is only known to belong to some uncertainty set. Mathematics of operations research 26 2, 193205, 2001. Idea behind robust optimization is to consider the worst cas e scenario without a speci c distribution assumption. The themes range across various areas of optimization. Robust convex optimization 1998 mathematics of operations research. Robust optimisation math bibliographies cite this for me. He has been a leader in continuous optimization and is best known for his work on the ellipsoid method, modern interiorpoint methods and robust optimization. Arkadi nemirovski born march 14, 1947 is a professor at the h. Robust optimization is an important subfield of optimization that deals with uncer tainty in.
In the following, ben tal and nemirovskis results on costs are generalized to smooth convex conic problems under lipschitz uncertainty, given reasonably mild regularity conditions. Bertsimas, ben tal, elghaoui, nemirovski 1990snow ee364b, stanford university 1. Ben tal and nemirovski 8 studied robust optimization applied to conic quadratic and semide. Robust optimization is still a relatively new approach to optimization problems affected by uncertainty. A robust optimization approach to supply chain management. The book is published by princeton university press, august 2009, see here. Robust optimization also makes an ideal graduate textbook on the subject. In addition to surveying the direct applications of robust optimization to machine learning, important in their own right, this chapter explores some.
The roots of robust optimization can be found in the eld of ro bust control and in the work of soyster 9 as well as later works by ben tal and nemirovski 1,2 and independently by elghaoui and lebret 6 and elg haoui et al 7. In the main part of the paper we show that if u is an ellipsoidal uncertainty set, then for some of the most important generic convex optimization problems linear programming, quadratically constrained programming, semidefinite programming and others the corresponding robust convex program is either exactly, or approximately, a tractable. Surprisingly, for the netlibproblems these robust solutions nearly lose nothing in optimality. The paper surveys the main results of ro as applied to uncertain linear, conic quadratic and semidefinite programming. Ben tal and nemirovski approach to robust optimization consider the linear program min ct x p8 subject to ax. Uncertain linear optimization problems and their robust counterparts. Nemirovski, on approximate robust counterparts of uncertain semidefinite and conic quadratic programs proceedings of 20th ifip tc7 conference on system modelling and optimization, july 2327, 2001, trier, germany 3. An essential book for anyone working on optimization and decision making under uncertainty, robust optimization also makes an ideal graduate textbook on the subject. Theory and applications of robust optimization citeseerx.
Furthermore, ben tal and nemirovski 8 studied robust optimization applied to conic quadratic and semide. For these cases, computationally tractable robust counterparts of. Nemirovski, arkadi published by princeton university press on. Save up to 80% by choosing the etextbook option for isbn. Robust optimization for emergency logistics planning. Robust optimization princeton series in applied mathematics 9780691143682. Download for offline reading, highlight, bookmark or take notes while you read robust optimization. Applications of robust linear and nonlinear optimization in engineering.
Ben tal and nemirovski,, introduced a number of important formulations and applications, and provided a detailed analysis of the robust optimization framework in linear programming and general convex programming. We study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u, yet the constraints must hold for all possible values of the data from u. The ensuing optimization problem is called robust optimization. Aharon bental is an emeritus professor of operations research and former dean of the faculty of industrial engineering and management at the technion israel institute of. Robust optimization princeton series in applied mathematics series by aharon ben tal. Professor ben tal was awarded in 2007 the euro gold medal and was named informs fellow in 2010. For example, it has been used successfully to address. A summary of their results can be found in the book btgn09. A practical guide to robust optimization sciencedirect. Nemirovski, arkadi and a great selection of similar new, used and collectible books available now at great prices.
The book is published by princeton university press, august 2009, see. Furthermore, the book has been structured so that the first part could easily be used as the text for a graduate level course in robust optimization. Over the last two decades, robust optimization ro has emerged as a popular approach for decisionmaking under uncertainty in singlestage settings, see e. Robust solutions of uncertain linear programs sciencedirect. Similar to the approach of stochastic optimization, robust optimization deals. In this paper we lay the foundation of robust convex optimization. Pdf robust optimizationmethodology and applications. This book is devoted to robust optimization a specific and relatively. Robust optimization princeton series in applied mathematics hardcover by ben tal, aharon. Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Brown y, constantine caramanis z july 6, 2007 abstract in this paper we survey the primary research, both theoretical and applied, in the. Robust optimization is designed to meet some major challenges associated with uncertaintyaffected optimization problems.
Robust convex optimization mathematics of operations research. Robust linear optimization under general norms sciencedirect. Robust optimization is a young and active research field that has been mainly developed in the last 15 years. Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering. Robust convex optimization mathematics of operations. Our focus will be on the computational attractiveness of ro approaches, as well. Robust optimization made easy with rome 974 operations research 594, pp. System modeling and optimization xx deals with new developments in the areas of optimization, optimal control and system modeling. Robust optimization is very useful for practice, since it is tailored to the information at hand, and it leads to computationally tractable formulations. Part of the lecture notes in computer science book series lncs, volume 3064. Theory and applications of robust optimization dimitris bertsimas. Unfortunately there is few books that deals with robust optimization.
Robust optimization princeton series in applied mathematics 9780691143682 by ben tal, aharon. This book is an authoritative reference that will be very useful to researchers working in this area. Drafts of selected chapters from the book robust optimization in progress by ben tal, a. Pdf theory and applications of robust optimization researchgate. Robust optimization ro isa modeling methodology, combined with computational tools, to. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and uptodate account.
902 1364 1426 551 895 1467 401 1181 164 1470 48 1280 195 4 1083 813 1061 618 422 158 1020 1620 128 739 102 1064 1437 4 755 501 298 531 1193 780 1367 729 255 1217 1155 419 403 399 517 274 566