On finite-dimensional generalized variational inequalities

Barbara Panicucci; Massimo Pappalardo; Mauro Passacantando

doi:10.3934/jimo.2006.2.43

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2006, Volume 2, Issue 1: 43-53. Doi: 10.3934/jimo.2006.2.43

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On finite-dimensional generalized variational inequalities

1.
Department of Applied Mathematics - University of Pisa, via Bonanno, 25/b, 56126 Pisa

Received: April 30, 2005

Revised: November 30, 2005

Published: December 2005

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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).

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Mathematics Subject Classification: 49J40, 49J53, 90C30.

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