Journal of Optimization Theory and Applications

, Volume 140, Issue 1, pp 103-116

First online:

Expected Residual Minimization Method for Stochastic Variational Inequality Problems

  • M. J. LuoAffiliated withDepartment of Applied Mathematics, Dalian University of Technology
  • , G. H. LinAffiliated withDepartment of Applied Mathematics, Dalian University of Technology Email author 

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This paper considers a stochastic variational inequality problem (SVIP). We first formulate SVIP as an optimization problem (ERM problem) that minimizes the expected residual of the so-called regularized gap function. Then, we focus on a SVIP subclass in which the function involved is assumed to be affine. We study the properties of the ERM problem and propose a quasi-Monte Carlo method for solving the problem. Comprehensive convergence analysis is included as well.


Stochastic variational inequalities Level sets Quasi-Monte Carlo methods Convergence