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Volumetric barrier decomposition algorithms for two-stage stochastic linear semi-infinite programming

Baha Alzalg(baha2math***at***gmail.com)
Asma Gafour(asma gafour***at***yahoo.fr)
Lewa’ Alzaleq(lewa.alzaleq***at***wsu.edu)

Abstract: In this paper, we study the two-stage stochastic linear semi-infinite programming with recourse to handle uncertainty in data defining (deterministic) linear semi-infinite programming. We develop and analyze volumetric barrier decomposition-based interior point methods for solving this class of optimization problems, and present a complexity analysis of the proposed algorithms. We establish our convergence analysis by showing that the volumetric barrier associated with the recourse function of stochastic linear semi-infinite programs is a strongly self-concordant barrier and forms a self-concordant family on the first-stage solutions. The dominant terms in the complexity expressions obtained in this paper are given in terms of the problem dimension and the number of realizations. The novelty of our algorithms lies in their ability to kill the effect of the radii of the largest Euclidean balls contained in the feasibility sets on the dominant complexity terms.

Keywords: Semi-infinite programming, Stochastic linear programming, Interior point methods, Volumetric barrier, Decomposition

Category 1: Infinite Dimensional Optimization (Semi-infinite Programming )

Category 2: Stochastic Programming

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

Citation: Rochester Institute of Technology, December 2018

Download: [PDF]

Entry Submitted: 12/06/2018
Entry Accepted: 12/06/2018
Entry Last Modified: 12/06/2018

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