Two-stage stochastic variational inequalities: an ERM-solution procedure

Xiaojun Chen, Ting Kei Pong, Roger J.B. Wets

Research output: Journal article publicationJournal articleAcademic researchpeer-review

36 Citations (Scopus)


We propose a two-stage stochastic variational inequality model to deal with random variables in variational inequalities, and formulate this model as a two-stage stochastic programming with recourse by using an expected residual minimization solution procedure. The solvability, differentiability and convexity of the two-stage stochastic programming and the convergence of its sample average approximation are established. Examples of this model are given, including the optimality conditions for stochastic programs, a Walras equilibrium problem and Wardrop flow equilibrium. We also formulate stochastic traffic assignments on arcs flow as a two-stage stochastic variational inequality based on Wardrop flow equilibrium and present numerical results of the Douglas–Rachford splitting method for the corresponding two-stage stochastic programming with recourse.
Original languageEnglish
Pages (from-to)71-111
Number of pages41
JournalMathematical Programming
Issue number1
Publication statusPublished - 1 Sept 2017


  • Expected residual minimization
  • Regularized gap function
  • Splitting method
  • Stochastic program with recourse
  • Stochastic variational inequalities
  • Wardrop equilibrium

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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