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: The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs.
Abstract: In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed.
260 citations
01 Jan 2006
TL;DR: The purpose of this tutorial is to present a mathematical framework that is well-suited to the limited information available in real-life problems and captures the decision-maker’s attitude towards uncertainty; the proposed approach builds upon recent developments in robust and data-driven optimization.
Abstract: Traditional models of decision-making under uncertainty assume perfect information, i.e., accurate values for the system parameters and speciflc probability distributions for the random variables. However, such precise knowledge is rarely available in practice, and a strategy based on erroneous inputs might be infeasible or exhibit poor performance when implemented. The purpose of this tutorial is to present a mathematical framework that is well-suited to the limited information available in real-life problems and captures the decision-maker’s attitude towards uncertainty; the proposed approach builds upon recent developments in robust and data-driven optimization. In robust optimization, random variables are modeled as uncertain parameters belonging to a convex uncertainty set and the decision-maker protects the system against the worst case within that set. Data-driven optimization uses observations of the random variables as direct inputs to the mathematical programming problems. The flrst part of the tutorial describes the robust optimization paradigm in detail in single-stage and multi-stage problems. In the second part, we address the issue of constructing uncertainty sets using historical realizations of the random variables and investigate the connection between convex sets, in particular polyhedra, and a speciflc class of risk measures.
260 citations
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TL;DR: In this paper, a mathematical formulation for optimal planning of a developed EH considering operation constraints is presented for deterministic and stochastic circumstances of wind power, electricity price, and the hub electricity demand.
258 citations
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TL;DR: It is shown that, under mild regularity conditions, such a min-max problem generates a probability distribution on the set of permissible distributions with the min- max problem being equivalent to the expected value problem with respect to the corresponding weighted distribution.
Abstract: In practical applications of stochastic programming the involved probability distributions are never known exactly. One can try to hedge against the worst expected value resulting from a considered set of permissible distributions. This leads to a min-max formulation of the corresponding stochastic programming problem. We show that, under mild regularity conditions, such a min-max problem generates a probability distribution on the set of permissible distributions with the min-max problem being equivalent to the expected value problem with respect to the corresponding weighted distribution. We consider examples of the news vendor problem, the problem of moments and problems involving unimodal distributions. Finally, we discuss the Monte Carlo sample average approach to solving such min-max problems.
258 citations