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
A robust optimization model under uncertain environment: An application in production planning
TL;DR: This work addressed an uncertain linear programming problem in which some constraints involves the product of two uncertain parameters that are robust in nature and established an equivalent approximation of the robust counterpart of such types of uncertain programming problems.
Dissertation
Adaptive Robust Optimization with Applications in Inventory and Revenue Management
TL;DR: In this paper, the authors propose a hierarchy of polynomial policies that are also directly parameterized in the observed uncertainties, and that can be efficiently computed using semidefinite optimization methods.
DissertationDOI
Effective and efficient coordination of flexibility in smart grids
TL;DR: In this paper, the authors propose a method to plan such a system based on the simulation of the dispatch process, where the planning result determines the configuration of a controller, and place these methods in a general model.
Journal ArticleDOI
Complexity Results and Effective Algorithms for Worst-Case Linear Optimization Under Uncertainties
TL;DR: The so-called worst-case linear optimization (WCLO) with uncertainties on the right-hand side of the constraints is considered, which often arises in applications such as in s...
Journal ArticleDOI
A VNS-LP algorithm for the robust dynamic maximal covering location problem
TL;DR: This study introduces a robust variant of the well-known dynamic maximal covering location problem (DMCLP) and proposes an integer linear programming formulation of the robust DMCLP, which is based on hybridization of a Variable neighborhood search and a linear programming technique.
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