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
FAST-Fast Algorithm for the Scenario Technique.
TL;DR: The Fast Algorithm for the Scenario Technique is introduced, a variant of the scenario optimization algorithm with reduced sample complexity, to obtain feasible solutions to chance-constrained optimization problems based on random sampling.
Journal ArticleDOI
On nonsmooth robust multiobjective optimization under generalized convexity with applications to portfolio optimization
TL;DR: A new concept of generalized convexity at a given point for a family of real-valued functions and deduce nonsmooth sufficient optimality conditions for robust (weakly) efficient solutions is introduced.
Journal ArticleDOI
Robust closed-loop supply chain design with presorting, return quality and carbon emission considerations
TL;DR: A deterministic mathematical model and its robust variant are proposed to investigate the effects of the quality of returns on the CLSC network under the carbon cap (CC) and carbon cap-and-trade (CCT) policies.
Proceedings ArticleDOI
Analysis of the impact of sensor noise on formation flying control
TL;DR: Modifications are presented to the station-keeping optimization algorithms that have been developed using linear programming to account for sensing errors, which robustified the design of the control inputs to velocity errors, but this is achieved at the expense of using much shorter design horizons.
Journal ArticleDOI
On the applicability and solution of bilevel optimization models in transportation science: A study on the existence, stability and computation of optimal solutions to stochastic mathematical programs with equilibrium constraints
TL;DR: This work considers natural stochastic extensions to a class of MPEC traffic models which explicitly incorporate data uncertainty, and establishes not only the existence of optimal solutions, but in particular their stability to perturbations in the probability distribution.
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