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Clustering-Based Preconditioning for Stochastic Programs

Yankai Cao (cao142***at***purdue.edu)
Carl D. Laird (lairdc***at***purdue.edu)
Victor M Zavala (vzavala***at***mcs.anl.gov)

Abstract: We present a clustering-based preconditioning strategy for KKT systems arising in stochastic programming within an interior-point framework. The key idea is to perform adaptive clustering of scenarios (inside-the-solver) based on their influence on the problem as opposed to cluster scenarios based on problem data alone, as is done in existing (outside-thesolver) approaches. We derive spectral and error properties for the preconditioner and demonstrate that scenario compression rates of up to 87% can be obtained, leading to dramatic computational savings. In addition, we demonstrate that the proposed preconditioner can avoid scalability issues of Schur decomposition in problems with large first-stage dimensionality.

Keywords: preconditioning; large-scale; stochastic; clustering

Category 1: Stochastic Programming

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Linear, Cone and Semidefinite Programming (Linear Programming )


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Entry Submitted: 12/16/2014
Entry Accepted: 12/16/2014
Entry Last Modified: 11/08/2015

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