IJPAM: Volume 63, No. 1 (2010)

MERIT FUNCTIONS AND EQUIVALENT DIFFERENTIABLE
OPTIMIZATION PROBLEMS FOR THE EXTENDED
GENERAL VARIATIONAL INEQUALITIES

Min Sun
Department of Mathematics and Information Science
Zaozhuang University
Shandong, 277160, P.R. CHINA
e-mail: [email protected]


Abstract.In this paper, we study some merit functions and equivalent differentiable optimization problems for the extended general variational inequalities involving three operators, which was introduced and studied by M.A. Noor (see [#!1!#]) very recently. Using the projection technique, we obtain some error bounds for the solution of extended general variational inequalities under some mild conditions, and then formulate the extended general variational inequalities as differentiable constrained (or unconstrained) optimization problems. We also prove that the extended general variational inequalities have a unique solution under some conditions.

Received: May 4, 2010

AMS Subject Classification: 90C30, 90C33

Key Words and Phrases: extended general variational inequalities, merit functions, error bounds

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 1