Abstract.In this paper we use the penalty approach in order to study two constrained minimization problems. A penalty function is said to have the exact penalty property if there is a penalty coefficient for which a solution of an unconstrained penalized problem is a solution of the corresponding constrained problem. In this paper we establish the existence of the exact penalty for an equality-constrained problem and an inequality-constrained problem in a Banach space.

Received: May 12, 2006

AMS Subject Classification: 49M30, 90C26, 90C30

Key Words and Phrases: Clarke's generalized gradient, Ekeland's variational principle, minimization problem, penalty function

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 2