Descent methods for a class of generalized variational inequalities

Authors:
Barbara Panicucci;Massimo Pappalardo;Mauro Passacantando
Affiliations:
Department of Applied Mathematics, University of Pisa, Pisa, Italy 56127;Department of Applied Mathematics, University of Pisa, Pisa, Italy 56127;Department of Applied Mathematics, University of Pisa, Pisa, Italy 56127
Venue:
Computational Optimization and Applications
Year:
2010

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Abstract

In this paper we propose a class of differentiable gap functions in order to formulate a generalized variational inequality (GVI) problem, involving a set-valued map with closed and convex graph, as an optimization problem. We also show that under appropriate assumptions on the set-valued map, any stationary point of the equivalent optimization problem is a global optimal solution and solves the GVI. Finally, we describe descent methods for solving the optimization problem equivalent to the GVI and we prove its global convergence.