Excellent surveys of the literature on robust optimization are available in beyer and sendho 12. Nus business school, national university of singapore. Robust and reliable portfolio optimization formulation of. Nemirovski we study convex optimization problems for which the data is not speci ed 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. Robust and reliable portfolio optimization formulation of a. Save up to 80% by choosing the etextbook option for isbn. More specifically, bental and nemirovski 2000 show that the radius of the ellipsoidal uncertainty, which is denoted by. Our worstcase approach is inspired from the literature of robust optimization ben tal et al. Robust convexoptimization ben tal andnemirovski 1997, elghaoui et. After analyzing the robust program as well with respect to stability. Robust optimization ro is a recent optimization approach that deals with data uncertainty.
The optimization community, however, was relatively quiet on the issue of robustness until the work of bental and nemirovski e. 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. Compared to the traditionalscenariobased stochastic programming method, robust counterpart optimization method has a unique advantage, in that the scale of the corresponding optimization problem does not increase exponentially with the number of the uncertain parameters. Ifip tc7 20th conference on system modeling and optimization july 2327, 2001, trier, germany springer us aharon ben tal, arkadi nemirovski auth. Tilburg university adjustable robust optimization zhen, jianzhe. Michael poss introduction to robust optimization may 30, 2017 9 53. Arkadi nemirovski and publisher princeton university press. This robust technique has obtained prodigious success since the late 1990s, especially in the. Tractable approximations to robust conic optimization problems.
Whereas stochastic programming assumes there is a probabilistic description of the uncertainty, robust optimization works with a deterministic, setbased description of the uncertainty. Aharon ben tal arkadi nemirovski robust optimization methodology and applications received. Nemirovski 15 proposed tractable approximation in the form of an sdp if. For a detailed overview of the ro framework, we refer to bental et al. Robust optimization is designed to meet some major challenges associated with uncertaintyaffected optimization problems. Robust optimization of system design sciencedirect. Robust optimization belongs to an important methodology for dealing with optimization problems with data uncertainty. Language english format pdf pages 576 isbn 9781400831050 file size 8. The goal of this paper therefore is to develop such a framework. Recent works using this general approach include bental and nemirovski1998,1999,2000,bertsimasandsim2004.
Recent advances in robust optimization optimization online. Aug 10, 2009 robust optimization is designed to meet some major challenges associated with uncertaintyaffected optimization problems. 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. Robust optimization for process scheduling under uncertainty. Robust optimization ro is a modeling methodology, combined with. An exact algorithm for twostage robust optimization with mixed integer recourse problems.
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. Bental and nemirovski approach to robust optimization consider the linear program min ct x p8 subject to ax. The robust optimization method, which focused on treatability of computation in the case of data points disturbing in convex sets, was first proposed by soyster 2 and developed, respectively, by. Robust optimization methodology and applications springerlink. Aharon ben tal is professor of operations research at the. The computational bottleneck associated with robust optimization was addressed in several papers. Robust counterpart formulations for linear optimization. Furthermore, ben tal and nemirovski 8 studied robust optimization applied to conic quadratic and semide.
September 12, 2001 published online february 14, 2002 springerverlag 2002 abstract. Aharon ben tal is professor of operations research at the technion, israel institute for technology. A robust optimization perspective on stochastic programming. Section 3 describes important new directions in robust optimization, in particular multistage adaptable robust optimization, which is much less developed, and rich with open questions. Robust optimization is a young and active research. This approach dates back to soyster 1973, who considered a deterministic linear optimization model that is feasible for all data lying in a convex set. Stochastic optimization starts by assuming the uncertainty has a. Robust optimization is a methodology that can be applied to problems. Sep 21, 2011 one major motivation for studying robust optimization is that in many applications the data set is an appropriate notion of parameter uncertainty, e. In the robust optimization framework the problem solved is a minmax problem where a solution is judged according to its performance on the worst possible realization of the parameters. Ro methodology can be applied to any generic optimization problem where one can separate uncertain numerical data from the problems structure. Nemirovski we study convex optimization problems for which the data is not speci. Robust optimization by aharon bental overdrive rakuten. Robust convexoptimization bental andnemirovski 1997, elghaoui et.
An exact algorithm for twostage robust optimization with. A soft robust model for optimization under ambiguity 1222 operationsresearch584,part2of2,pp. A robust optimization approach for humanitarian needs. How positive psychology can maximize your impact and make you happier in a challenging world. Pdf robust optimizationmethodology and applications. Furthermore, bental and nemirovski 8 studied robust optimization applied to conic quadratic and semide. Theory and applications of robust optimization dimitris bertsimas. Sim nusdistributionally robust optimization26 aug 2009 4 47. An essential book for anyone working on optimization and decision making under uncertainty, robust optimization also makes an ideal graduate textbook on the subject. Robust optimization made easy with rome joel goh stanford graduate school of business.
Additionally, basic versions of ro assume hard constraints, i. Ben tal and nemirovski 7 propose a robust optimization model to immunize a portfolio against the uncertainty in the asset returns. Experiments in robust optimization columbia university. In the ben tal robust optimization book, the approach is called, constraintwise. In section 4, we detail a wide spectrum of application areas to illustrate the broad impact that robust optimization has had in the early part of its development. The support of the uncertain parameters is referred to as uncertainty set. Robust optimization ro methodology uses chance and robust constraints to generate a robust solution immunized against the effect of data uncertainty. View conic quadratic program from ise 5014 at vellore institute of technology. Robust optimization in countably in nite linear programs. Robust optimization ro, on the other hand, does not assume that probability distributions are known, but instead it assumes that the uncertain data resides in a socalled uncertainty set. In this section, we will be looking at the basic case of robust linear programming. We also show how the notion of a budget of uncertainty enters into several di.
Robust optimization ro isa modeling methodology, combined with computational tools, to. Theory and applications of robust optimization the university of. The paper surveys the main results of ro as applied to uncertain linear, conic quadratic and semidefinite programming. Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. Two existing approaches within the dro framework that address the conservatism of robust optimization are soft robust optimization ben tal et al. These studies all assume that the distribution of the random parameters is supported on a nite set of values and the ambiguity set is constructed for the discrete distribution.
Robust optimization is an important subfield of optimization that deals with uncer tainty in. For these cases, computationally tractable robust counterparts of. Contrast with classical robust optimization ro uncertainties in ro characterized by uncertainty set support ben tal and nemirovski 1998, bertsimas and sim 2004 j. Recent works using this general approach include ben tal and nemirovski1998,1999,2000,bertsimasandsim2004. Distributionally robust optimization and its tractable. Pdf theory and applications of robust optimization researchgate.
Proceedings of 20 th ifip tc7 conference on system modelling and optimization, july 2327, trier, germany, 2001b. Robust optimization with application in asset management. 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. Ben tal and nemirovski approach to robust optimization consider the linear program min ct x p8 subject to ax. Tilburg university globalized robust optimization for. This decision rule approximation transforms the original dynamic problem to a static robust optimization problem whose decision variables are the coe.
This paper addresses the uncertainty problem in process scheduling using robust optimization. Robust optimization and applications stanford university. With respect to portfolio selection, the major contributions. Robust optimization is a relatively new approach to modeling uncertainty in optimization problems. 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. The ensuing optimization problem is called robust optimization. Robust optimization, robustness, adaptable optimization, applications of robust op. This is done by introducing an uncertainty set for the parameters and performing a worstcase optimization. Two existing approaches within the dro framework that address the conservatism of robust optimization are soft robust optimization bental et al. Robust optimization models aim to nd the best decision in view of the worstcase parameter aluesv within these sets.
1590 646 628 1353 1151 1001 101 968 1356 1298 218 843 359 151 1505 662 464 298 1113 64 1071 1597 975 553 388 594 1069 698 767 1224 258 1208