IJPAM: Volume 103, No. 3 (2015)

CONSISTENCY ANALYSIS OF AUBIN PROPERTY OF
SAA SOLUTION MAPPING FOR A STOCHASTIC
COMPLEMENTARITY PROBLEM

Yu-Xin Li$^1$, Jie Zhang$^2$, Zun-Quan Xia$^3$
$^{1,3}$School of Mathematical Science
Dalian University of Technology
Dalian, 116024, P.R. CHINA
$^2$School of Mathematics
Liaoning Normal University
Dalian, 116029, P.R. CHINA


Abstract. In this paper, we investigate properties of sample average approximation (SAA) solution mapping for a parametric stochastic complementarity problem, where the underlying function is the expected value of stochastic function. In particular, using the notion of cosmic deviation, which is originated from the concept of cosmic distance in variational analysis, we develop sufficient conditions for the consistency of Aubin property of the solution mapping of the SAA parametric stochastic complementarity problems, namely if the solution map of the true problem has the Aubin property around some point, then so does the SAA problem around reference point with probability one when the sample size is large enough. At last, an example is illustrated to show the application of the analysis.

Received: May 8, 2015

AMS Subject Classification: 90C30

Key Words and Phrases: sample average approximation, parametric stochastic complementarity problem, Aubin property

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DOI: 10.12732/ijpam.v103i3.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 3
Pages: 499 - 510


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