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Expected Residual Minimization Method for Stochastic Variational Inequality Problems

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, Dalian University of Technology, Dalian, 116024, China

    M. J. Luo & G. H. Lin

Authors
  1. M. J. Luo
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  2. G. H. Lin
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Corresponding author

Correspondence to G. H. Lin.

Additional information

Communicated by M. Fukushima.

This work was supported in part by SRF for ROCS, SEM and Project 10771025 supported by NSFC.

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Luo, M.J., Lin, G.H. Expected Residual Minimization Method for Stochastic Variational Inequality Problems. J Optim Theory Appl 140, 103–116 (2009). https://doi.org/10.1007/s10957-008-9439-6

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  • DOI: https://doi.org/10.1007/s10957-008-9439-6

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