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
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The State of Robust Optimization
Seçil Sözüer,Aurélie Thiele +1 more
TL;DR: This survey presents a broad overview of the developments in robust optimization over the past 5 years, i.e., between 2011 and 2015, and describes novel findings in static and multi-stage decision making, the connection with stochastic optimization, distributional robustness and robust nonlinear optimization.
Journal ArticleDOI
A robust optimization approach for itinerary planning with deadline
Yu Zhang,Yu Zhang,Jiafu Tang +2 more
TL;DR: A robust optimization approach to address the itinerary planning problem with deadline in public transit networks that maximizes the size of the uncertainty set of arc travel times, while guaranteeing that the corresponding worst-case arrival time of itinerary would not exceed the deadline.
Journal ArticleDOI
Least-cost design of water distribution systems under demand uncertainty: the robust counterpart approach
TL;DR: In this paper, a non-probabilistic robust counterpart (RC) approach is demonstrated and applied to the least-cost design/rehabilitation problem of water distribution systems (WDSs), the uncertainty of the information is described by a deterministic user-defined ellipsoidal uncertainty set that implies the level of risk.
Journal ArticleDOI
Robust Optimization of Fourth Party Logistics Network Design under Disruptions
TL;DR: It is indicated that the robust optimization model can evade the market risks effectively and save the cost in the maximum limit when it is applied to 4PL network design.
Posted Content
Improved Decision Rule Approximations for Multi-Stage Robust Optimization via Copositive Programming
Guanglin Xu,Grani A. Hanasusanto +1 more
TL;DR: This work proposes decision rule approximations for generic multi-stage robust linear optimization problems that are NP-hard but amenable to copositive programming reformulations that give rise to tight conservative approxIMations.
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