Primal interior-point decomposition algorithms for two-stage stochastic extended second-order cone programming. (2nd December 2018)

• Record Type: Journal Article
• Authors: Alzalg, Baha
• Is Part Of: Optimization. Volume 67:Number 12(2018)
• Page Start: 2291
• Page End: 2323
• Publication Date: 2018-12-02
• Subjects: Extended second order cone -- conic programming -- stochastic programming -- interior-point algorithms -- self-concordance; 90C15 -- 90C22 -- 90C30 -- 90C51; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1533553
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We study and solve the two-stage stochastic extended second-order cone programming problem. We show that the barrier recourse functions and the composite barrier functions for this optimization problem are self-concordant families with respect to barrier parameters. These results are used to develop primal decomposition-based interior-point algorithms. The worst case iteration complexity of the developed algorithms is shown to be the same as that for the short- and long-step primal interior algorithms applied to the extensive formulation of our problem.