Stability analysis of stochastic programs with second order dominance constraints

• 成果类型: Article
• 署名作者: Liu, Yongchao; Xu, Huifu
• 署名单位: Dalian Maritime University; University of Southampton
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-012-0585-0
• 发表日期: 2013
• 页码: 435-460
• 关键词: quantitative stability; optimization problems; large numbers; error-bounds; CONVERGENCE; LAWS

摘要

In this paper we present a stability analysis of a stochastic optimization problem with stochastic second order dominance constraints. We consider a perturbation of the underlying probability measure in the space of regular measures equipped with pseudometric discrepancy distance (Romisch in Stochastic Programming. Elsevier, Amsterdam, pp 483-554, 2003). By exploiting a result on error bounds in semi-infinite programming due to Gugat (Math Program Ser B 88:255-275, 2000), 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 an empirical probability measure and show an exponential rate of convergence of the sequence of optimal solutions obtained from solving the approximation problem. The analysis is extended to the stationary points.