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Stochastic programming

About: Stochastic programming is a research topic. Over the lifetime, 12343 publications have been published within this topic receiving 421049 citations.


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Journal ArticleDOI
TL;DR: The extension of Robust Optimization methodology developed in this paper opens up new possibilities to solve efficiently multi-stage finite-horizon uncertain optimization problems, in particular, to analyze and to synthesize linear controllers for discrete time dynamical systems.
Abstract: In this paper, we propose a new methodology for handling optimization problems with uncertain data. With the usual Robust Optimization paradigm, one looks for the decisions ensuring a required performance for all realizations of the data from a given bounded uncertainty set, whereas with the proposed approach, we require also a controlled deterioration in performance when the data is outside the uncertainty set.The extension of Robust Optimization methodology developed in this paper opens up new possibilities to solve efficiently multi-stage finite-horizon uncertain optimization problems, in particular, to analyze and to synthesize linear controllers for discrete time dynamical systems.

227 citations

Journal Article
TL;DR: This book provides a unified framework based on a sensitivity point of view and introduces new approaches and proposes new research topics within this sensitivity-based framework.
Abstract: Performance optimization is vital in the design and operation of modern engineering systems, including communications, manufacturing, robotics, and logistics. Most engineering systems are too complicated to model, or the system parameters cannot be easily identified, so learning techniques have to be applied. This book provides a unified framework based on a sensitivity point of view. It also introduces new approaches and proposes new research topics within this sensitivity-based framework. This new perspective on a popular topic is presented by a well respected expert in the field.

226 citations

Journal ArticleDOI
TL;DR: In this article, a general approach susceptible of individual variations, depending upon the problem and the judgment of the user, is presented, and two moderate-size examples are presented to illustrate the method.
Abstract: : This paper considers optimization problems in which some or all variables must take on integral values. An ability to solve such problems would be valuable in itself and would also allow handling certain kinds of heretofore intractable 'economies of scale'. An automatic algorithm for solving such problems is not given. A general approach susceptible of individual variations, depending upon the problem and the judgment of the user is presented. Two moderate-size examples are presented to illustrate the method. (Author)

226 citations

Journal ArticleDOI
TL;DR: A pre-disaster planning problem that seeks to strengthen a highway network whose links are subject to random failures due to a disaster is addressed and it is shown that using the first order terms of this function leads to a knapsack problem whose solution is a local optimum to the original problem.

226 citations

01 Jan 2012
TL;DR: The main contribution of the paper is to show that the KL divergence constrained DRO problems are often of the same complexity as their original stochastic programming problems and, thus, KL divergence appears a good candidate in modeling distribution ambiguities in mathematical programming.
Abstract: In this paper we study distributionally robust optimization (DRO) problems where the ambiguity set of the probability distribution is defined by the Kullback-Leibler (KL) divergence. We consider DRO problems where the ambiguity is in the objective function, which takes a form of an expectation, and show that the resulted minimax DRO problems can be formulated as a one-layer convex minimization problem. We also consider DRO problems where the ambiguity is in the constraint. We show that ambiguous expectation-constrained programs may be reformulated as a one-layer convex optimization problem that takes the form of the Benstein approximation of Nemirovski and Shapiro (2006). We further consider distributionally robust probabilistic programs. We show that the optimal solution of a probability minimization problem is also optimal for the distributionally robust version of the same problem, and also show that the ambiguous chance-constrained programs (CCPs) may be reformulated as the original CCP with an adjusted confidence level. A number of examples and special cases are also discussed in the paper to show that the reformulated problems may take simple forms that can be solved easily. The main contribution of the paper is to show that the KL divergence constrained DRO problems are often of the same complexity as their original stochastic programming problems and, thus, KL divergence appears a good candidate in modeling distribution ambiguities in mathematical programming.

225 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023175
2022423
2021526
2020598
2019578
2018532