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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An inexact fuzzy-robust two-stage programming model for managing sulfur dioxide abatement under uncertainty
TL;DR: Results indicate that useful solutions for planning the air quality management practices have been generated and can help decision makers identify desired pollution-abatement strategy with minimized system cost and maximized environmental efficiency.
Journal ArticleDOI
A tight characterization of the performance of static solutions in two-stage adjustable robust linear optimization
TL;DR: Bertsimas et al. as discussed by the authors study the performance of static solutions for two-stage adjustable robust linear optimization problems with uncertain constraint and objective coefficients and give a tight characterization of the adaptivity gap.
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Robust Rate Maximization Game Under Bounded Channel Uncertainty
TL;DR: It is proved that increasing channel uncertainty can lead to a more efficient equilibrium and, hence, a better sum rate in certain two-user communication systems and this improvement in equilibrium efficiency is also observed in systems with a higher number of users.
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TRusT: A Two-stage Robustness Trade-off approach for the design of decentralized energy supply systems
TL;DR: It is shown that energy supply systems with guaranteed secure energy supply are not expensive per se and the Two-stage Robustness Trade-off (TRusT) approach is a suitable tool to design cost-efficient and secure energy systems.
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.
Related Papers (5)
Robust solutions of Linear Programming problems contaminated with uncertain data
Aharon Ben-Tal,Arkadi Nemirovski +1 more