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.

Panicucci, B., Pappalardo, M., Passacantando, M. (2010). Descent methods for a class of generalized variational inequalities. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 45(2), 415-425 [10.1007/s10589-008-9230-5].

Descent methods for a class of generalized variational inequalities

Passacantando, M
2010

Abstract

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.
Articolo in rivista - Articolo scientifico
Descent method; Gap function; Generalized variational inequality; Set-valued map;
English
415
425
11
Panicucci, B., Pappalardo, M., Passacantando, M. (2010). Descent methods for a class of generalized variational inequalities. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 45(2), 415-425 [10.1007/s10589-008-9230-5].
Panicucci, B; Pappalardo, M; Passacantando, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/391545
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