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A Warm-Start Approach for Large-Scale Stochastic Linear Programs

Marco Colombo (m.colombo***at***ed.ac.uk)
Jacek Gondzio (j.gondzio***at***ed.ac.uk)
Andreas Grothey (a.grothey***at***ed.ac.uk)

Abstract: We describe a method of generating a warm-start point for interior point methods in the context of stochastic programming. Our approach exploits the structural information of the stochastic problem so that it can be seen as a structure-exploiting initial point generator. We solve a small-scale version of the problem corresponding to a reduced event tree and use the solution to generate an advanced starting point for the complete problem. The way we produce a reduced tree tries to capture the important information in the scenario space while keeping the dimension of the corresponding (reduced) deterministic equivalent small. We derive conditions which should be satisfied by the reduced tree to guarantee a successful warm-start of the complete problem. The implementation within the HOPDM and OOPS interior point solvers shows remarkable advantages.

Keywords: Warm-Start, Interior Point Methods, Stochastic Linear Programming

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 2: Stochastic Programming

Citation: Technical Report MS-06-004, School of Mathematics, The University of Edinburgh, 29 August 2006, revised 4 May 2007

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Entry Submitted: 08/29/2006
Entry Accepted: 08/29/2006
Entry Last Modified: 05/04/2007

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