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SPEPS Preprint

Author(s): Yongchao Liu, Dalian Maritime University
Werner Römisch, Humboldt-University
Huifu Xu, University of Southampton
Title: Quantitative Stability Analysis of Stochastic Generalized Equations
Date of Acceptance: 13.10.2012
Submission Date: 15.06.2012
Series Title: Stochastic Programming E-Print Series
(SPEPS)
Editors: Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint: pdf (urn:nbn:de:kobv:11-100204906)
Keywords (eng): stability analysis, stochastic semi-infinite programming, stochastic generalized equations, equicontinuity, one stage stochastic programs, two stage stochastic programs, tow stage SMPCs
Appeared in: SIAM Journal on Optimization 24 (2014)
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Abstract (eng):
We consider the solution of a system of stochastic generalized equations (SGE) where the underlying functions are mathematical expectation of random set-valued mappings. SGE has many applications such as characterizing optimality conditions of a nonsmooth stochastic optimization problem and a stochastic equilibrium problem. We derive quantitative continuity of expected value of the set-valued mapping with respect to the variation of the underlying probability measure in a metric space. This leads to the subsequent qualitative and quantitative stability analysis of solution set mappings of the SGE. Under some metric regularity conditions, we derive Aubin’s property of the solution set mapping with respect to the change of probability measure. The established results are applied to stability analysis of stationary points of classical one stage and two stage stochastic minimization problems, two stage stochastic mathematical programs with equilibrium constraints and stochastic programs with second order dominance constraints.
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