On Generalized Monotone Multifunctions with Applications to Optimality Conditions in Generalized Convex Programming

Volume 4, Issue 4, 2003

Article 67

ON GENERALIZED MONOTONE MULTIFUNCTIONS WITH APPLICATIONS TO OPTIMALITY CONDITIONS IN GENERALIZED CONVEX PROGRAMMING

A. HASSOUNI AND A. JADDAR

DÉPARTEMENT DE MATH\'EMATIQUES ET D'INFORMATIQUE,
FACULTÉ DES SCIENCES,
B.P. 1014, RUE IBN BATOUTA,
RABAT, MAROC.
E-Mail: hassounia@hotmail.com

Received 29 May, 2002; Accepted 16 March, 2003.
Communicated by: Z. Nashed

ABSTRACT. Characterization of quasiconvexity and pseudoconvexity of lower semicontinuous functions on Banach spaces are presented in terms of abstract subdifferentials relying on a Mean Value Theorem. We give some properties of the normal cone to the lower level set of f. We also obtain necessary and sufficient optimality conditions in quasiconvex and pseudoconvex programming via variational inequalities.

Key words:
Generalized monotone multifunction, Generalized convex function, Quasiconvex, Pseudoconvex, Generalized subdifferentials, Normal cone, Level set, Local minimum, Global minimum, Variational inequalities.

2000 Mathematics Subject Classification:
90C26, 26B25, 47H04.

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