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

Yong Zhao (), Jin Zhang, Xinmin Yang and Gui-Hua Lin
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Yong Zhao: Sichuan University
Jin Zhang: Hong Kong Baptist University
Xinmin Yang: Chongqing Normal University
Gui-Hua Lin: Shanghai University

Journal of Optimization Theory and Applications, 2017, vol. 175, issue 2, No 13, 545-566

Abstract: 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.

Keywords: Stochastic vector variational inequalities; Expected residual minimization formulation; Sample average approximation; 90C33; 90C15 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-0939-5

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