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Existence of Approximate Exact Penalty in Constrained Optimization

Department of Mathematics, The Technion-Israel Institute of Technology, 32000 Haifa, Israel
ajzasl{at}tx.technion.ac.il

In this paper, we use the penalty approach in order to study constrained minimization problems in infinite dimensional spaces. 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 exact penalty property for a large class of inequality-constrained minimization problems.

Key Words: approximate solution; Ekeland’s variational principle; minimization problem; penalty function
History: Received: February 8, 2005; revision received: March 19, 2006;