An inexact Newton method for stationary points of mathematical programs constrained by parameterized quasi-variational inequalities

Indexed by:Journal Papers

Date of Publication:2015-08-01

Journal:NUMERICAL ALGORITHMS

Included Journals:Scopus、SCIE

Volume:69

Issue:4

Page Number:713-735

ISSN:1017-1398

Key Words:Inexact Newton method; MPEC; Optimality conditions; Strongly BD-regularity

Abstract:In this paper, we propose a numerical method for solving the stationary points of mathematical programs constrained by parameterized quasi-variational inequalities. The necessary optimality conditions (stationary conditions in the sense of Mordukhovich) for the optimization problem are reformulated as a system of nonsmooth equations without the strict complementarity condition and an inexact Newton method is constructed to find its solutions. The local convergence of the inexact Newton method is guaranteed under second order sufficient conditions and linear independence constraint qualification. Several illustrative examples are provided.