A Homogeneous Predictor-Corrector Algorithm for Stochastic Nonsymmetric Convex Conic Optimization With Discrete Support

Baha Alzalg (baha2mathgmail.com)
Mohammad Alabedalhadi (mhm9140083fgs.ju.edu.jo)

Abstract: We consider a stochastic convex optimization problem over nonsymmetric cones with discrete support. This class of optimization problems has not been studied yet. By using a logarithmically homogeneous self-concordant barrier function, we present a homogeneous predictor-corrector interior-point algorithm for solving stochastic nonsymmetric conic optimization problems. We also derive an iteration bound for the proposed algorithm. Our main result is that we uniquely combine a nonsymmetric algorithm with efficient methods for computing the predictor and corrector directions. Finally, we describe a realistic application and present computational results for instances of the stochastic facility location problem formulated as a stochastic nonsymmetric convex conic optimization problem.

Keywords: Convex optimization; Nonsymmetric programming; Stochastic programming; Predictor-corrector methods; Interior point methods.

Category 1: Linear, Cone and Semidefinite Programming

Category 2: Stochastic Programming

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Entry Submitted: 06/14/2021
Entry Accepted: 06/14/2021
Entry Last Modified: 11/22/2021

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