Generalized Quasi-Variational Inequalities and Duality

Volume 4, Issue 2, 2003

Article 28

GENERALIZED QUASI-VARIATIONAL INEQUALITIES AND DUALITY

DIPARTIMENTO DI MATEMATICA E STATISTICA
UNIVERSITÀ DI NAPOLI FEDERICO II
VIA CINTHIA, 80126 NAPOLI, ITALY.
E-Mail: morgan@unina.it

DIPARTIMENTO DI ORGANIZZAZIONE AZIENDALE E AMMINISTRAZIONE PUBBLICA
UNIVERSITÀ DELLA CALABRIA
VIA PIETRO BUCCI, 87036 COSENZA, ITALY.
E-Mail: mromanie@unina.it

Received 18 November, 2002; Accepted 4 February, 2003.
Communicated by: A.M. Rubinov

ABSTRACT. We present a scheme which associates to a generalized quasi-variational inequality a dual problem and generalized Kuhn-Tucker conditions.
This scheme allows to solve the primal and the dual problems in the spirit of the classical Lagrangian duality for constrained optimization problems and extends, in non necessarily finite dimentional spaces, the duality approach obtained by A. Auslender for generalized variational inequalities. An application to social Nash equilibria is presented together with some illustrative examples.

Key words:
Generalized quasi-variational inequality, Primal and dual problems, Generalized Kuhn-Tucker conditions, Banach space, Social Nash equilibrium, Subdifferential.

2000 Mathematics Subject Classification:
65K10, 49N15, 91A10.

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