Robust solutions of uncertain linear programs
Aharon Ben-Tal,Arkadi Nemirovski +1 more
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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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Book ChapterDOI
Robustness in Multi-criteria Decision Aiding
Hassene Aissi,Bernard Roy +1 more
TL;DR: This chapter introduces the concept of variable setting, which serves to connect what is defined as the formal representation of the decision-aiding problem and the real-life decisional context, and introduces five typical problems that will serve as reference problems in the rest of the chapter.
Journal ArticleDOI
A robust optimization approach for airport departure metering under uncertain taxi-out time predictions
TL;DR: In this paper, a robust optimization approach for metering aircraft departures under uncertainty in the taxi-out process is presented, where a mixed integer linear programming model for runway sequencing and scheduling that incorporates uncertainty sets for the taxiout time is proposed in order to dynamically determine an optimal and robust sequence and schedule of aircraft release from the gate.
Journal ArticleDOI
A two-step infinite α-cuts fuzzy linear programming method in determination of optimal allocation strategies in agricultural irrigation systems.
TL;DR: The proposed TSIFP can be noted as the first attempt in solving FLP without any unreasonable simplification and assumption, and it is indicated that, due to the constraints being relaxed in FRLP, more water beyond the system’s capacity would be over-allocated for pursuing higher system benefits, implying the unreliability of F RLP in being extended to real-world practices.
Journal ArticleDOI
Nonlinear robust optimization via sequential convex bilevel programming
Boris Houska,Moritz Diehl +1 more
TL;DR: A conservative approximation strategy for nonlinear inequality constrained robust optimization problems and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties.
Proceedings ArticleDOI
Monotonicity of dissipative flow networks renders robust maximum profit problem tractable: General analysis and application to natural gas flows
TL;DR: It is proved that potentials are monotonic functions of the withdrawals, which enables to replace in the maximum profit optimization infinitely many nodal constraints, each representing a particular value of withdrawal uncertainty, by only two constraints representing the cases where all nodes with uncertainty consume their minimum and maximum amounts respectively.
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