Expected Residual Minimization Formulation for a Class of Stochastic Vector Variational Inequalities

Yong Zhao*, Jin ZHANG, Xinmin Yang, Gui Hua Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

This paper considers a class of vector variational inequalities. First, we present an equivalent formulation, which is a scalar variational inequality, for the deterministic vector variational inequality. Then we concentrate on the stochastic circumstance. By noting that the stochastic vector variational inequality may not have a solution feasible for all realizations of the random variable in general, for tractability, we employ the expected residual minimization approach, which aims at minimizing the expected residual of the so-called regularized gap function. We investigate the properties of the expected residual minimization problem, and furthermore, we propose a sample average approximation method for solving the expected residual minimization problem. Comprehensive convergence analysis for the approximation approach is established as well.

Original languageEnglish
Pages (from-to)545-566
Number of pages22
JournalJournal of Optimization Theory and Applications
Volume175
Issue number2
DOIs
Publication statusPublished - 1 Nov 2017

Scopus Subject Areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

User-Defined Keywords

  • Expected residual minimization formulation
  • Sample average approximation
  • Stochastic vector variational inequalities

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