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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Vehicle positioning in cell manufacturing systems via robust optimization
TL;DR: Two new zero-one programming (ZOP) models for vehicle positioning in multi-cell automated manufacturing system and the robust counterpart of the proposed ZOP models is presented by using the recent extensions in robust optimization theory.
Robust Runway Scheduling using a time-indexed model
TL;DR: This approach transforms the planning problem into an assignment problem with side constraints and results in fewer sequence changes and target time updates compared to the usual approach of just updating the plan if the actual plan is not feasible any more.
BookDOI
Integration of AI and OR Techniques in Constraint Programming
TL;DR: This work proposes a technique to strengthen a relaxed decision diagram of a problem by incorporating inference from constraints via a Lagrangian relaxation method, and associates penalties with the constraints that may be potentially violated by the solutions encoded in a relaxable decision diagram.
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Varying confidence levels for CVaR risk measures and minimax limits
TL;DR: This paper proposes a procedure to explore the possibility of varying the confidence level to a lower value which can give an advantage when there is a need to find good solutions to CVaR-constrained problems out of sample.
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Regularized robust optimization: the optimal portfolio execution case
TL;DR: A regularized robust optimization formulation is proposed which yields a solution with a better stability property than the classical robust solution, and implications of the regularization on the optimal execution strategy and its corresponding execution cost are studied.
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