Application of Fenchel's Duality Theorem to Penalty Methods in Convex Programming

Abstract

This paper studies a new class of sequential unconstrained optimization methods, called the conjugate penalty method, for solving convex programming problems. The validity of the method is based on Fenchel's duality theorem. It is shown that, under certain condi- tions, conjugate penalty founctins are uniformly bounded on a neighborhood of a point which is an optimum of Fenchel's dual problem.