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 design framework relies entirely on deterministic direct and sensitivity analysis of the continuum systems, thereby significantly enhancing the range of applicability of the framework for the design in the presence of uncertainty of many other systems usually analyzed with legacy codes.
102 citations
TL;DR: This work proposes decomposition frameworks for handling CVaR objectives and constraints in two-stage stochastic models and proposes special Level-type methods for the solution of the decomposed problems.
102 citations
TL;DR: In this paper, the authors present a robust optimization tool for storage investment on transmission networks, which employs robust optimization to minimize the investment in storage units, without load or renewable power curtailment, for all scenarios in the convex hull of a discrete uncertainty set.
Abstract: This paper discusses the need for the integration of storage systems on transmission networks having renewable sources, and presents a tool for energy storage planning. The tool employs robust optimization to minimize the investment in storage units that guarantee a feasible system operation, without load or renewable power curtailment, for all scenarios in the convex hull of a discrete uncertainty set; it is termed ROSION—Robust Optimization of Storage Investment On Networks. The computa- tional engine in ROSION is a specific tailored implementation of a column-and-constraint generation algorithm for two-stage robust optimization problems, where a lower and an upper bound on the optimal objective function value are successively calculated until convergence. The lower bound is computed using mixed-integer linear programming and the upper bound via linear programming applied to a sequence of similar problems. ROSION is demon- strated for storage planning on the IEEE 14-bus and 118-bus networks, and the robustness of the designs is validated via Monte Carlo simulation.
102 citations
TL;DR: The combined augmented Lagrangian/barrier method applies in a natural way to stochastic programming and multicommodity networks.
101 citations
TL;DR: Stability and sensitivity studies for stochastic programs have been motivated by the problem of incomplete information about the true probability measure through which the Stochastic program is formulated and in connection with the development and evaluation of algorithms as mentioned in this paper.
Abstract: Stability and sensitivity studies for stochastic programs have been motivated by the problem of incomplete information about the true probability measure through which the stochastic program is formulated and in connection with the development and evaluation of algorithms. The first part of this survey paper briefly introduces and compares different approaches and points out the contemporary efforts to remove and weaken assumptions that are not realistic (e.g., strict complementarity conditions). The second part surveys recent results on qualitative and quantitative stability with respect to the underlying probability measure and describes the ways and means of statistical sensitivity analysis based on Gâteaux derivatives. The last section comments on parallel statistical sensitivity results obtained in the parametric case, i.e., for probability measures belonging to a parametric family indexed by a finite dimensional vector parameter.
101 citations