Stability and sensitivity analysis of stochastic programs with second order dominance constraints

Yongchao Liu; Huifu Xu

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SPEPS Preprint

Author(s):	Yongchao Liu, Dalian University of Technology Huifu Xu, University of Southampton
Title:	Stability and sensitivity analysis of stochastic programs with second order dominance constraints
Date of Acceptance:	25.05.2010
Submission Date:	17.06.2010
Series Title:	Stochastic Programming E-Print Series (SPEPS)
Editors:	Julie L. Higle; Werner Römisch; Surrajeet Sen
Complete Preprint:	pdf (urn:nbn:de:kobv:11-100174214)
Keywords (eng):	sample average approximation, Lipschitz stability, second order dominance, stochastic semi-infinite programming, error bound
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Abstract (eng):

In this paper we present stability and sensitivity analysis of a stochastic optimization problem with stochastic second order dominance constraints. We consider perturbation of the underlying probability measure in the space of regular measures equipped with pseudometric discrepancy distance ( [30]). By exploiting a result on error bound in semi-inﬁnite programming due to Gugat [13], we show under the Slater constraint qualiﬁcation that the optimal value function is Lipschitz continuous and the optimal solution set mapping is upper semicontinuous with respect to the perturbation of the probability measure. In particular, we consider the case when the probability measure is approximated by empirical probability measure and show the exponential rate of convergence of optimal solution obtained from solving the approximation problem. The analysis is extended to the stationary points when the objective function is nonconvex.

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