CVAR-based formulation and approximation method for stochastic variational inequalities

Xiaojun Chen, Guihua Lin

Research output: Journal article publicationJournal articleAcademic researchpeer-review

14 Citations (Scopus)

Abstract

In this paper, we study the stochastic variational inequality problem (SVIP) from a viewpoint of minimization of conditional value-at-risk. We employ the D-gap residual function for VIPs to define a loss function for SVIPs. In order to reduce the risk of high losses in applications of SVIPs, we use the D-gap function and conditional value-at-risk to present a deterministic minimization reformulation for SVIPs. We show that the new reformulation is a convex program under suitable conditions. Furthermore, by using the smoothing techniques and the Monte Carlo methods, we propose a smoothing approximation method for finding a solution of the new reformulation and show that this method is globally convergent with probability one.
Original languageEnglish
Pages (from-to)35-48
Number of pages14
JournalNumerical Algebra, Control and Optimization
Volume1
Issue number1
DOIs
Publication statusPublished - 1 Feb 2011

Keywords

  • Conditional value at risk
  • Convergence
  • D-gap function
  • Monte Carlo sampling approximation
  • Smoothing approximation
  • Stochastic variational inequalities

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Control and Optimization
  • Applied Mathematics

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