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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Journal ArticleDOI
Advanced Robust Optimization With Interval Uncertainty Using a Single-Looped Structure and Sequential Quadratic Programming
Jianhua Zhou,Mian Li +1 more
Book ChapterDOI
Layered formulation for the robust vehicle routing problem with time windows
Agostinho Agra,Marielle Christiansen,Rosa Figueiredo,Lars Magnus Hvattum,Michael Poss,Cristina Requejo +5 more
TL;DR: This paper presents an extended formulation for the vehicle routing problem with time windows that allows the classical (static) robust programming approach to the problem to be applied.
Journal ArticleDOI
Mechanisms for information elicitation
TL;DR: This work examines elicitation mechanisms that elicit the confidence rating of the seller regarding its information and provides two very different exponential-time algorithms for the design problem that have different asymptotic running times.
Journal ArticleDOI
A two-stage robust optimization approach for the mobile facility fleet sizing and routing problem under uncertainty
Chao Lei,Wei-Hua Lin,Lixin Miao +2 more
TL;DR: A two-level cutting plane based method is developed, which includes an algorithm to generate problem-specific lower bound inequalities in the outer level, and a hybrid algorithm in the inner level that combines heuristic and exact methods to solve the recourse problem.
Journal ArticleDOI
Distributed robust optimization (DRO), part I: framework and example
TL;DR: This paper discusses several models for describing parameter uncertainty sets that can lead to decomposable problem structures and thus distributed solutions and applies these models in solving a robust rate control problem in wireline networks.
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