Descent methods for a class of generalized variational inequalities.

Panicucci, Barbara; Pappalardo, Massimo; Passacantando, Mauro

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.

DIFFERENTIAL inequalities; MATHEMATICAL optimization; GRAPHIC methods; CALCULUS of variations; TOPOLOGICAL spaces; SET-valued maps

Computational Optimization & Applications, 2010, Vol 45, Issue 2, p415

0926-6003

Academic Journal

10.1007/s10589-008-9230-5