Stability and sensitivity analysis of stochastic programs with second order dominance constraints
Stability and sensitivity analysis of stochastic programs with second order dominance constraints
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.
sample average approximation, lipschitz stability, second order dominance, stochastic semi-infinite programming, error bound
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Higle, Julie E.
bd5b61dd-3487-497d-ad8b-edfeaf22ef01
Romisch, Werner
62eb88a7-12aa-4ea4-bc5e-b7cb6bb222a8
17 June 2010
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Higle, Julie E.
bd5b61dd-3487-497d-ad8b-edfeaf22ef01
Romisch, Werner
62eb88a7-12aa-4ea4-bc5e-b7cb6bb222a8
Liu, Yongchao and Xu, Huifu
,
Higle, Julie E. and Romisch, Werner
(eds.)
(2010)
Stability and sensitivity analysis of stochastic programs with second order dominance constraints.
Stochastic Programming E-Print Series.
Abstract
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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Liu-Xu--17-June-2010.pdf
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Submitted date: 25 May 2010
Published date: 17 June 2010
Keywords:
sample average approximation, lipschitz stability, second order dominance, stochastic semi-infinite programming, error bound
Organisations:
Operational Research
Identifiers
Local EPrints ID: 182199
URI: http://eprints.soton.ac.uk/id/eprint/182199
PURE UUID: 873f6eb8-7bf8-4c0d-83a7-1a427f089e07
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Date deposited: 27 Apr 2011 14:56
Last modified: 15 Mar 2024 03:15
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Contributors
Author:
Yongchao Liu
Author:
Huifu Xu
Editor:
Julie E. Higle
Editor:
Werner Romisch
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