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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Scheduling production for a sawmill: A robust optimization approach
TL;DR: This paper considers the problem of scheduling production under uncertainty in a sawmill, where the deterministic model proposed by Maturana et al. (2010) was extended to account for uncertainties in product demand and availability of raw materials.
Journal ArticleDOI
A copositive approach for two-stage adjustable robust optimization with uncertain right-hand sides
Guanglin Xu,Samuel Burer +1 more
TL;DR: In this article, the affine policy is reformulated as a copositive optimization problem, which leads to a class of tractable, semidefinite-based approximations.
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Robust optimization framework for cardinality constrained portfolio problem
TL;DR: This paper proposes a new portfolio modeling approach with uncertain data and it is also analyzed using different robust optimization techniques and the proposed formulations are solved using genetic algorithm.
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Robust data envelopment analysis approaches for evaluating algorithmic performance
TL;DR: This work considers each algorithm as a decision-making unit (DMU) and develops robust data envelopment analysis (DEA) models taking into account not only average but also standard deviation of an algorithm's output for evaluating relative efficiencies of a set of algorithms.
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A log-robust optimization approach to portfolio management
Ban Kawas,Aurélie Thiele +1 more
TL;DR: The results indicate that the Log-robust approach significantly outperforms the benchmark with respect to 95 or 99% Value-at-Risk, because the traditional robust approach leads to portfolios that are far less diversified.
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