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

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 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 (Römisch 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.
0025-5610
435-460
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Liu, Yongchao
e7721a8a-028e-42b2-ac67-e30a0d3a2cf7
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5

Liu, Yongchao and Xu, Huifu (2013) Stability and sensitivity analysis of stochastic programs with second order dominance constraints. Mathematical Programming, 142 (1), 435-460. (doi:10.1007/s10107-012-0585-0).

Record type: Article

Abstract

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 (Römisch 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.

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More information

e-pub ahead of print date: 23 August 2012
Published date: December 2013
Organisations: Operational Research

Identifiers

Local EPrints ID: 390726
URI: http://eprints.soton.ac.uk/id/eprint/390726
ISSN: 0025-5610
PURE UUID: 1ade3cc9-e1e5-485c-b24c-2e489589a3d9
ORCID for Huifu Xu: ORCID iD orcid.org/0000-0001-8307-2920

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Date deposited: 06 Apr 2016 14:18
Last modified: 08 Jan 2022 02:57

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Contributors

Author: Yongchao Liu
Author: Huifu Xu ORCID iD

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