Exact Penalty Functions in Constrained Optimization

Abstract

In this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated, thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions. In this framework the best-known classes of exact penalty functions are analyzed, and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions.