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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.


Papers
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Journal ArticleDOI
TL;DR: In this article, a stochastic multi-objective linear programming problem is formulated to find the optimized operation strategies of the DER system to reduce the expected energy costs and CO2 emissions, while satisfying the time-varying user demand.

190 citations

Journal ArticleDOI
TL;DR: This work defines a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion and shows that the aggregate satisfies sharp oracle inequalities under some general assumptions.
Abstract: Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion. We define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original nonlinear one and constitutes a special case of the mirror averaging algorithm. We show that the aggregate satisfies sharp oracle inequalities under some general assumptions. The results are applied to several problems including regression, classification and density estimation.

189 citations

Journal ArticleDOI
TL;DR: Time consistency of multistage risk averse stochastic programming problems is discussed and it is suggested that at each state of the system optimality of a decision policy should not involve states which cannot happen in the future.

188 citations

01 Jan 2007
TL;DR: Within the framework of multi-stage mixed-integer linear stochastic programming, a short-term production plan for a price-taking hydropower plant operating under uncertainty is developed.

188 citations

Book ChapterDOI
01 Sep 2015
TL;DR: This tutorial presents two-stage models with distributional uncertainty using phi-divergences and ties them to risk-averse optimization and examines the value of collecting additional data.
Abstract: Most of classical stochastic programming assumes that the distribution of uncertain parameters are known, and this distribution is an input to the model. In many applications, however, the true distribution is unknown. An ambiguity set of distributions can be used in these cases to hedge against the distributional uncertainty. Phi-divergences (Kullback–Leibler divergence, χ-distance, etc.) provide a measure of distance between two probability distributions. They can be used in data-driven stochastic optimization to create an ambiguity set of distributions that are centered on a nominal distribution. The nominal distribution can be determined by collected observations, expert opinions, simulations, etc. Many phi-divergences are widely used in statistics; therefore they provide a natural way to create an ambiguity set of distributions from available data and expert opinions. In this tutorial, we present two-stage models with distributional uncertainty using phi-divergences and tie them to risk-averse optimization. We examine the value of collecting additional data. We present a classification of phi-divergences to elucidate their use for models with different sources of data and decision makers with different risk preferences. We illustrate these ideas on several examples.

188 citations


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