A sample average approximation method based on a D-gap function for stochastic variational inequality problems

He, Suxiang; Zhang, Pan; Hu, Xiao; Hu, Rong

doi:10.3934/jimo.2014.10.977

Cited by 7 publications

(2 citation statements)

References 24 publications

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“…Moreover, considering (21) and the fact that̂( ) , converges to ( ) with probability one as → ∞, we have that (3) (̂( ) , ,̂, ( ), ) converges to (3) ( ( ) , ( ), ) with probability one uniformly on ( * , ) as → ∞. Thus, from the above analyses of (A), (B) and (C), we draw the conclusion that ( ) converges to ( ) with probability one uniformly on ( * , ) as → ∞.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

“…sample 1 , ⋅ ⋅ ⋅ , of the random variable ∈ Ξ with sample size by Monte Carlo sampling method and approximate the involved expected value functions in problem (1) by their corresponding sample average functions. The SAA method 2 Mathematical Problems in Engineering has drawn much attention from many authors, see the comprehensive work by Shapiro [17] and the other works in [18][19][20][21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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An Implementable SAA Nonlinear Lagrange Algorithm for Constrained Minimax Stochastic Optimization Problems

Wang

2018

Mathematical Problems in Engineering

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This paper proposes an implementable SAA (sample average approximation) nonlinear Lagrange algorithm for the constrained minimax stochastic optimization problem based on the sample average approximation method. A computable nonlinear Lagrange function with sample average approximation functions of original functions is minimized and the Lagrange multiplier is updated based on the sample average approximation functions of original functions in the algorithm. And it is shown that the solution sequences obtained by the novel algorithm for solving subproblem converge to their true counterparts with probability one as the sample size approximates infinity under some moderate assumptions. Finally, numerical experiments are carried out for solving some typical test problems and the obtained numerical results preliminarily demonstrate that the proposed algorithm is promising.

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Section: Mathematical Problems In Engineeringmentioning

confidence: 99%