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
Optimized maritime emergency resource allocation under dynamic demand
TL;DR: A robust approach is developed and used to make sure that the resource allocation schedule performs well with dynamic demand, and a case study shows that the proposed methodology is feasible in maritime emergency resource allocation.
Dissertation
Strategic planning of aircraft trajectories
TL;DR: The proposed methodology aims at minimizing the global interaction between aircraft trajectories by allocating alternative departure times, alternative horizontal flight paths, and alternative flight levels to the trajectories involved in the interaction.
Journal ArticleDOI
Robust resource allocation scheme under channel uncertainties for LTE-A systems
TL;DR: An intelligent QoS-aware bandwidth allocation solution is proposed for the uplink traffic when the channel condition is uncertain and the numerical results show that the proposed scheme provides reliable scheduling for real-time services without harming the performance of non-real-time QoS parameters.
Journal ArticleDOI
Exact conic programming reformulations of two-stage adjustable robust linear programs with new quadratic decision rules
TL;DR: It is shown via numerical experiments on lot-sizing problems with uncertain demand that adjustable robust linear optimization problems with QDRs improve upon the ADRs in their performance both in the worst-case sense and after simulated realization of the uncertain demand relative to the true solution.
Journal ArticleDOI
Data driven matrix uncertainty for robust linear programming
A.L. Soyster,F.H. Murphy +1 more
TL;DR: The set of matrices also embed a covariance structure for the matrix coefficients and it is shown that when negative covariances predominate in the rows, more favorable optimal objective values for the primal can be expected.
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