Topic
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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TL;DR: This paper overviews several selected topics in this popular area, specifically, recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data, tractability of robust counterparts, links between RO and traditional chance constrained settings of problems with stochastic data, and a novel generic application of the RO methodology in Robust Linear Control.
Abstract: Robust Optimization is a rapidly developing methodology for handling optimization problems affected by non-stochastic “uncertain-but- bounded” data perturbations. In this paper, we overview several selected topics in this popular area, specifically, (1) recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data, (2) tractability of robust counterparts, (3) links between RO and traditional chance constrained settings of problems with stochastic data, and (4) a novel generic application of the RO methodology in Robust Linear Control.
339 citations
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TL;DR: The robust sampled problem is shown to be a good approximation for the ambiguous chance constrained problem with a high probability using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with ahigh probability.
Abstract: In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set ** of the distributions is of the form ** where ρp denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure **. The main contribution of this paper is to show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with a high probability. We also show that the robust sampled problem can be solved efficiently both in theory and in practice.
337 citations
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TL;DR: In this paper, a combined power management/design optimization problem for the performance optimization of FCHVs is formulated, which includes subsystem scaling models to predict the characteristics of components of different sizes, and a parameterizable and near-optimal controller for power management optimization.
334 citations
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TL;DR: The problem of measuring a network's maximum resilience level and simultaneously determining the optimal set of preparedness and recovery actions necessary to achieve this level under budget and level-of-service constraints is formulated as a two-stage stochastic program.
329 citations
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TL;DR: The robust design of a vibration absorber with mass and stiffness uncertainty in the main system is used to demonstrate the robust design approach in dynamics as discussed by the authors, and the results show a significant improvement in performance compared with the conventional solution.
328 citations