Nonconvex Quasi-Variational Inequalities: Stability Analysis and Application to Numerical Optimization

Joydeep Dutta (), Lahoussine Lafhim (), Alain Zemkoho () and Shenglong Zhou ()
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Joydeep Dutta: Indian Institute of Technology Kanpur
Lahoussine Lafhim: Sidi Mohammed Ben Abdellah University
Alain Zemkoho: University of Southampton
Shenglong Zhou: Beijing Jiaotong University

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 2, No 1, 43 pages

Abstract: 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.

Keywords: Quasi-variational inequalities; Stability analysis; Optimal value function; Optimization problems with quasi-variational inequality constraints; Semismooth Newton method; 90C26; 90C31; 90C33; 90C46; 90C55 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02582-4

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