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Extension and Implementation of Homogeneous Self-dual Methods for Symmetric Cones under Uncertainty

Baha Alzalg (b.alzalg***at***ju.edu.jo)
Francesca Maggioni (francesca.maggioni***at***unibg.it)
Sebastiano Vitali (sebastiano.vitali***at***unibg.it)

Abstract: Homogeneous self-dual algorithms for stochastic semidefinite programs with finite event space has been proposed by Jin et al. in [12]. Alzalg [8], has adopted their work to derive homogeneous self-dual algorithms for stochastic second-order programs with finite event space. In this paper, we generalize these two results to derive homogeneous self-dual algorithms for stochastic programs with finite event space over the much wider class of all symmetric cones. They include among others, stochastic semidefinite programs and stochastic second order cone programs. Special structure of the problem has been exploited to significantly reduce the computational burden. Numerical results on a simple test-case problem are finally presented for the homogeneous self-dual algorithm.

Keywords: Symmetric cone programming - Homogeneous self-dual algorithms - Computational complexity - Stochastic symmetric cone programming

Category 1: Stochastic Programming

Category 2: Linear, Cone and Semidefinite Programming

Citation: Published in Far East Journal of Mathematical Sciences, 99(11), 1603-1632.

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Entry Submitted: 03/06/2015
Entry Accepted: 03/06/2015
Entry Last Modified: 08/31/2016

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