Quantitative stability analysis of stochastic quasi-variational inequality problems and applications
Quantitative stability analysis of stochastic quasi-variational inequality problems and applications
We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is defined over the solution set of a parametric stochastic cone system. We investigate the impact of variation of the probability measure and the parameter on the solution of the SQVIP. By reformulating the SQVIP as a natural equation and treating the orthogonal projection over the solution set of the parametric stochastic cone system as an optimization problem, we effectively convert stability of the SQVIP into that of a one stage stochastic program with stochastic cone constraints. Under some moderate conditions, we derive Hölder outer semicontinuity and continuity of the solution set against the variation of the probability measure and the parameter. The stability results are applied to a mathematical program with stochastic semidefinite constraints and a mathematical program with SQVIP constraints.
Jie, Zhang
a677cc22-3082-4ac5-ac4b-7c7505f02df8
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Zhang, Liwei
10fce21c-16d9-4096-b07a-cf2cab1591c0
Jie, Zhang
a677cc22-3082-4ac5-ac4b-7c7505f02df8
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Zhang, Liwei
10fce21c-16d9-4096-b07a-cf2cab1591c0
Jie, Zhang, Xu, Huifu and Zhang, Liwei
(2017)
Quantitative stability analysis of stochastic quasi-variational inequality problems and applications.
Mathematical Programming.
(doi:10.1007/s10107-017-1116-9).
Abstract
We consider a parametric stochastic quasi-variational inequality problem (SQVIP for short) where the underlying normal cone is defined over the solution set of a parametric stochastic cone system. We investigate the impact of variation of the probability measure and the parameter on the solution of the SQVIP. By reformulating the SQVIP as a natural equation and treating the orthogonal projection over the solution set of the parametric stochastic cone system as an optimization problem, we effectively convert stability of the SQVIP into that of a one stage stochastic program with stochastic cone constraints. Under some moderate conditions, we derive Hölder outer semicontinuity and continuity of the solution set against the variation of the probability measure and the parameter. The stability results are applied to a mathematical program with stochastic semidefinite constraints and a mathematical program with SQVIP constraints.
Text
SQVIP_R3_06_Dec_2016
- Accepted Manuscript
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Accepted/In Press date: 25 January 2017
e-pub ahead of print date: 14 February 2017
Organisations:
Operational Research
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Local EPrints ID: 410156
URI: http://eprints.soton.ac.uk/id/eprint/410156
ISSN: 0025-5610
PURE UUID: 0f0ee3a6-5c5f-4515-976f-26623c69ab24
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Date deposited: 03 Jun 2017 04:04
Last modified: 16 Mar 2024 05:03
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Author:
Zhang Jie
Author:
Huifu Xu
Author:
Liwei Zhang
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