Solving quasi-variational inequalities via their KKT conditions

Abstract

We propose to solve a general quasi-variational inequality by using its Karush-Kuhn-Tucker conditions. To this end we use a globally convergent algorithm based on a potential reduction approach. We establish global convergence results for many interesting instances of quasi-variational inequalities, vastly broadening the class of problems that can be solved with theoretical guarantees. Our numerical testings are very promising and show the practical viability of the approach

RETRACTED: Canonical dual approach for contact mechanics problems with friction

“…[17] has been proved, when applied to this kind of problem, only for small values of the friction. In other words the analyzed examples with the value of the Coulomb friction F !…”

“…For what regards QVIs there are a few works devoted to the numerical solution of finite-dimensional QVIs (see e.g. [10][11][12][13][14][15][16]); in particular in the recent paper [17] a solution method for QVIs based on solving their Karush-Kuhn-Tucker (KKT) conditions is proposed.…”

Gap functions for quasi-equilibria

“…In [24] some classes of constraints are explicitly covered within KKT type methods for QVIs: moving set, box constraints, linear constraints with variable right-hand side, binary and bilinear constraints. The first three are covered in the framework of this paper too but the last two are not.…”

“…The first three are covered in the framework of this paper too but the last two are not. On the other side, Proposition 1 provides additional classes of constraints that have not been considered in [24].…”

“…Different approaches have been considered to devise solution methods: characterizations based on fixed points and projections [13,51,52], penalization of coupling constraints [55,57,22], KKT systems [24], minimization of dual gap functions in the affine case [36]. Also Newton type methods, which guarantee only local convergence, have been developed [53,54].…”