Expected Value and Sample Average Approximation Method for Solving Stochastic Second-Order Cone Complementarity Problems. (3rd July 2017)

• Record Type: Journal Article
• Authors: Luo, Mei-Ju; Zhang, Yan; Li, Ya-Jie
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 7(2017)
• Page Start: 911
• Page End: 925
• Publication Date: 2017-07-03
• Subjects: Convergence -- sample average approximation -- second-order cone -- smoothing function -- stochastic complementarity problems; 90C33 -- 65K05 -- 90C15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1300172
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we consider the stochastic second-order cone complementarity problems (SSOCCP). We first formulate the SSOCCP contained expectation as an optimization problem using the so-called second-order cone complementarity function. We then use sample average approximation method and smoothing technique to obtain the approximation problems for solving this reformulation. In theory, we show that any accumulation point of the global optimal solutions or stationary points of the approximation problems are global optimal solution or stationary point of the original problem under suitable conditions. Finally, some numerical examples are given to explain that the proposed methods are feasible.