Robust solutions of uncertain linear programs
Aharon Ben-Tal,Arkadi Nemirovski +1 more
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TLDR
It is shown that the RC of an LP with ellipsoidal uncertainty set is computationally tractable, since it leads to a conic quadratic program, which can be solved in polynomial time.About:
This article is published in Operations Research Letters.The article was published on 1999-08-01 and is currently open access. It has received 1809 citations till now. The article focuses on the topics: Uncertain data & Linear programming.read more
Citations
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Distributionally Robust Counterpart in Markov Decision Processes
Pengqian Yu,Huan Xu +1 more
TL;DR: In this paper, the authors adapt the distributionally robust optimization framework, assume that the uncertain parameters are random variables following an unknown distribution, and seek the strategy which maximizes the expected performance under the most adversarial distribution.
Journal ArticleDOI
Robust optimization for decision-making under endogenous uncertainty
TL;DR: This paper extends generic polyhedral uncertainty sets typically considered in robust optimization into sets that depend on the actual decisions, and shows how the use of these decision-dependent uncertainty sets allows to also eradicate conservatism effects from parameters that become irrelevant in view of the optimal decisions.
Journal ArticleDOI
Tractable approximate robust geometric programming
TL;DR: To overcome the “curse of dimensionality” that arises in directly approximating the nonlinear constraint functions in the original robust GP, it is shown how to find globally optimal PWL approximations of these bivariate constraint functions.
Posted ContentDOI
Robust Markov Decision Process: Beyond Rectangularity
TL;DR: The robust counterpart of important structural results of classical MDPs, including the maximum principle and Blackwell optimality, are introduced and a computational study is provided to demonstrate the effectiveness of the approach in mitigating the conservativeness of robust policies.
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Closed-loop supply chain network design and modelling under risks and demand uncertainty: an integrated robust optimization approach
TL;DR: RO based mathematical modeling to address risks and its applicability for SCND for close loop supply chain is proposed, demonstrated and applied in practical cases and shows that the topology obtained from integrated treatment of risk and uncertainty called as RORU model, outperform other supply chain networks on various network performance indicators.
References
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Book
Robust and Optimal Control
TL;DR: This paper reviewed the history of the relationship between robust control and optimal control and H-infinity theory and concluded that robust control has become thoroughly mainstream, and robust control methods permeate robust control theory.
BookDOI
Introduction to Stochastic Programming
John R. Birge,Franois Louveaux +1 more
TL;DR: This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability to help students develop an intuition on how to model uncertainty into mathematical problems.
Book
Interior-Point Polynomial Algorithms in Convex Programming
TL;DR: This book describes the first unified theory of polynomial-time interior-point methods, and describes several of the new algorithms described, e.g., the projective method, which have been implemented, tested on "real world" problems, and found to be extremely efficient in practice.
Journal ArticleDOI
Robust Convex Optimization
Aharon Ben-Tal,Arkadi Nemirovski +1 more
TL;DR: 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 problem which lends itself to efficientalgorithms such as polynomial time interior point methods.
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Robust solutions of Linear Programming problems contaminated with uncertain data
Aharon Ben-Tal,Arkadi Nemirovski +1 more