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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Proceedings ArticleDOI
Assessing regret-based preference elicitation with the UTPREF recommendation system
Darius Braziunas,Craig Boutilier +1 more
TL;DR: This work test both the effectiveness of regret-based elicitation, and user comprehension and acceptance of minimax regret in user studies, on a study involving 40 users interacting with the UTPref Recommendation System, which helps students navigate and find rental accommodation.
Journal ArticleDOI
Robust Linear Programming and Its Application to Water and Environmental Decision-Making under Uncertainty
TL;DR: A robust linear programming approach for water and environmental decision-making under uncertainty that is of significant practical utility to decision makers for obtaining reliable and robust management decisions that are “immune” to the uncertainty attributable to data perturbations.
Posted Content
Sparse Portfolio Selection via Quasi-Norm Regularization
TL;DR: A theory is presented that relates sparsity of the KKT points with Projected correlation and Projected Sharpe ratio, and an interior point algorithm is designed to obtain an approximate second-order KKT solution of the $\ell_p$-norm models in polynomial time with a fixed error tolerance.
Journal ArticleDOI
Designing a Reliable Multi-Objective Queuing Model of a Petrochemical Supply Chain Network under Uncertainty: A Case Study
Abolghasem Yousefi-Babadi,Reza Tavakkoli-Moghaddam,Reza Tavakkoli-Moghaddam,Reza Tavakkoli-Moghaddam,Ali Bozorgi-Amiri,S. Seifi +5 more
TL;DR: A multi-objectives mixed-integer non-linear programming (MINLP) model for a petrochemical supply chain under uncertainty environments, namely disruption risks and less knowledge of parameters is shown.
Journal ArticleDOI
Model Order Reduction Techniques with a Posteriori Error Control for Nonlinear Robust Optimization Governed by Partial Differential Equations
Oliver Lass,Stefan Ulbrich +1 more
TL;DR: An approximate robust formulation that employs linear and quadratic approximations to speed up the computation is proposed and is applied to the optimal placement of a permanent magnet in the rotor of a synchronous machine with moving rotor.
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