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).

Panicucci, B., Pappalrdo, M., Passacantando, M. (2006). On finite-dimensional generalized variational inequalities. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2(1), 43-53 [10.3934/jimo.2006.2.43].

On finite-dimensional generalized variational inequalities

Passacantando, M
2006

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).
No
Articolo in rivista - Articolo scientifico
Scientifica
Variational inequality; generalized variational inequality; equilibrium point; gap function
English
43
53
11
Panicucci, B., Pappalrdo, M., Passacantando, M. (2006). On finite-dimensional generalized variational inequalities. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2(1), 43-53 [10.3934/jimo.2006.2.43].
Panicucci, B; Pappalrdo, M; Passacantando, M
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/391535
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