Robust solutions of uncertain linear programs
Aharon Ben-Tal,Arkadi Nemirovski +1 more
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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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Peer ReviewDOI
Optimization models for supply chains under risk, uncertainty, and resilience: A state-of-the-art review and future research directions
TL;DR: A review of the quantitative models for SC resilience using bibliometric and network analyses is presented and highlights the inter-temporal dimensions of decision making and classifies articles based on their usability in real-world applications.
Posted Content
Monotonicity of Dissipative Flow Networks Renders Robust Maximum Profit Problem Tractable: General Analysis and Application to Natural Gas Flows
TL;DR: In this article, the authors consider general, steady, balanced flows of a commodity over a network where an instance of the network flow is characterized by edge flows and nodal potentials.
Journal ArticleDOI
A new equivalent transformation for interval inequality constraints of interval linear programming
TL;DR: According to the 3$$\upsigma $$σ law of normal distribution, a new equivalent transformation for constraints with the interval-valued coefficients of ILP is justified, and the uncertainty stemmed from interval number could be replaced by the uncertainty of random variables.
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Robust screening under ambiguity
Mustafa Ç. Pınar,Can Kızılkale +1 more
TL;DR: This work considers the problem of screening where a seller puts up for sale an indivisible good, and a buyer with a valuation unknown to the seller wishes to acquire the good and specifies four choices for the ambiguity set and derives the optimal mechanism in each case.
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Robust multiobjective optimization with application to Internet routing
TL;DR: The row-wise model is applied to an intradomain multiobjective routing problem with polyhedral traffic uncertainty and it is shown under additional assumptions that robust efficient solutions are efficient to specific instance problems and can be found as the efficient solutions of another deterministic problem.
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