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Computational aspects of risk-averse optimisation in two-stage stochastic models

Csaba Fabian (fabian.csaba***at***gamf.kefo.hu)

Abstract: In this paper we argue for aggregated models in decomposition schemes for two-stage stochastic programming problems. We observe that analogous schemes proved effective for single-stage risk-averse problems, and for general linear programming problems. A major drawback of the aggregated approach for two-stage problems is that an aggregated master problem can not contain all the information obtained by the solution of the second-stage problems. We observe that a recent proposal of Oliveira and Sagastiz\'abal eliminates this drawback. They propose storing all the second-stage information out of the master problem. They develop a family of approximate solution methods which, when applied to the aggregated master problem, can use the stored second-stage information. We develop a generalisation of the approximate level-type method of Oliveira and Sagastiz\'abal. The new method handles constraint functions in convex problems. It is based on the constrained level method of Lemarech\'al, Nemirovskii, and Nesterov, and on an inexact version. The new method can solve two-stage risk-averse problems. We show that aggregated models can be handled in a decomposition scheme without losing second-stage information.

Keywords: Stochastic programming, risk-averse models, convex programming, cutting-plane methods, linear programming, simplex method.

Category 1: Stochastic Programming

Category 2: Convex and Nonsmooth Optimization

Category 3: Linear, Cone and Semidefinite Programming


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Entry Submitted: 08/14/2012
Entry Accepted: 08/17/2012
Entry Last Modified: 02/12/2013

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