On finite-dimensional generalized variational inequalities

Pages: 43 - 53, Volume 2, Issue 1, February 2006

doi:10.3934/jimo.2006.2.43       Abstract        Full Text (207.7K)       Related Articles

Barbara Panicucci - Department of Applied Mathematics - University of Pisa, via Bonanno, 25/b, 56126 Pisa, Italy (email)
Massimo Pappalardo - Department of Applied Mathematics - University of Pisa, via Bonanno, 25/b, 56126 Pisa, Italy (email)
Mauro Passacantando - Department of Applied Mathematics - University of Pisa, via Bonanno, 25/b, 56126 Pisa, Italy (email)

Abstract: Our aim is to provide a short analysis of the generalized variational inequality (GVI) problem from both theoretical and algorithmic points of view. First, we show connections among some well known existence theorems for GVI and for inclusions. Then, we recall the proximal point approach and a splitting algorithm for solving GVI. Finally, we propose a class of differentiable gap functions for GVI, which is a natural extension of a well known class of gap functions for variational inequalities (VI).

Keywords:  Variational inequality, generalized variational inequality, equilibrium point, gap function.
Mathematics Subject Classification:  49J40, 49J53, 90C30.

Received: May 2005;      Revised: December 2005;      Published: January 2006.