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January  2006, 2(1): 43-53. doi: 10.3934/jimo.2006.2.43

On finite-dimensional generalized variational inequalities

Barbara Panicucci 1, , Massimo Pappalardo 1, and  Mauro Passacantando 1,

1. 

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

Received  May 2005 Revised  December 2005 Published  January 2006

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: generalized variational inequality, Variational inequality, equilibrium point, gap function..
Mathematics Subject Classification: 49J40, 49J53, 90C3.
Citation: Barbara Panicucci, Massimo Pappalardo, Mauro Passacantando. On finite-dimensional generalized variational inequalities. Journal of Industrial & Management Optimization, 2006, 2 (1) : 43-53. doi: 10.3934/jimo.2006.2.43
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