Nonconvex quasi-variational inequalities: stability analysis and application to numerical optimization
Nonconvex quasi-variational inequalities: stability analysis and application to numerical optimization
We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of optimal value function, we transform the problem into that of solving a nonsmooth system of inequalities. Based on this reformulation, new coderivative estimates as well as robust stability conditions for the optimal solution map of this QVI are developed. Also, for an optimization problem with QVI constraint, necessary optimality conditions are constructed and subsequently, a tailored semismooth Newton-type method is designed, implemented, and tested on a wide range of optimization examples from the literature. In addition to the fact that our approach does not require convexity, its coderivative and stability analysis do not involve second order derivatives, and subsequently, the proposed Newton scheme does not need third order derivatives, as it is the case for some previous works in the literature.
Quasi-variational inequalities, Semismooth Newton method, optimal value function, · Optimization problems with quasi-variational inequality constraints, · Stability analysis, Optimization problems with quasi-variational inequality constraints, Optimal value function, Stability analysis
Dutta, Joydeep
df58d72d-916d-4305-bdf3-53db3b46f50e
Lafhim, Lahoussine
91f799b8-61c7-4ed6-b8f1-ccf6b6e220fc
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Zhou, Shenglong
c2a1291b-d4bc-407b-bf1b-03861f1ecf2d
6 January 2025
Dutta, Joydeep
df58d72d-916d-4305-bdf3-53db3b46f50e
Lafhim, Lahoussine
91f799b8-61c7-4ed6-b8f1-ccf6b6e220fc
Zemkoho, Alain
30c79e30-9879-48bd-8d0b-e2fbbc01269e
Zhou, Shenglong
c2a1291b-d4bc-407b-bf1b-03861f1ecf2d
Dutta, Joydeep, Lafhim, Lahoussine, Zemkoho, Alain and Zhou, Shenglong
(2025)
Nonconvex quasi-variational inequalities: stability analysis and application to numerical optimization.
Journal of Optimization Theory and Applications, 204 (16), [16].
(doi:10.1007/s10957-024-02582-4).
Abstract
We consider a parametric quasi-variational inequality (QVI) without any convexity assumption. Using the concept of optimal value function, we transform the problem into that of solving a nonsmooth system of inequalities. Based on this reformulation, new coderivative estimates as well as robust stability conditions for the optimal solution map of this QVI are developed. Also, for an optimization problem with QVI constraint, necessary optimality conditions are constructed and subsequently, a tailored semismooth Newton-type method is designed, implemented, and tested on a wide range of optimization examples from the literature. In addition to the fact that our approach does not require convexity, its coderivative and stability analysis do not involve second order derivatives, and subsequently, the proposed Newton scheme does not need third order derivatives, as it is the case for some previous works in the literature.
Text
2210.02531v2
- Accepted Manuscript
Restricted to Repository staff only until 6 January 2026.
Request a copy
More information
Accepted/In Press date: 23 October 2024
Published date: 6 January 2025
Keywords:
Quasi-variational inequalities, Semismooth Newton method, optimal value function, · Optimization problems with quasi-variational inequality constraints, · Stability analysis, Optimization problems with quasi-variational inequality constraints, Optimal value function, Stability analysis
Identifiers
Local EPrints ID: 498407
URI: http://eprints.soton.ac.uk/id/eprint/498407
ISSN: 0022-3239
PURE UUID: 3984859f-ba11-4eac-a130-62d1f8d85cf5
Catalogue record
Date deposited: 18 Feb 2025 17:33
Last modified: 22 Aug 2025 02:12
Export record
Altmetrics
Contributors
Author:
Joydeep Dutta
Author:
Lahoussine Lafhim
Author:
Shenglong Zhou
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics
