A new exact exponential penalty function method and nonconvex mathematical programming

Abstract

A new exact penalty function method, called the l 1 exact exponential penalty function method, is introduced. In this approach, the so-called the exponential penalized optimization problem with the l 1 exact exponential penalty function is associated with the original optimization problem with both inequality and equality constraints. The l 1 exact exponential penalty function method is used to solve nonconvex mathematical programming problems with r-invex functions (with respect to the same function η). The equivalence between sets of optimal solutions of the original mathematical programming problem and of its associated exponential penalized optimization problem is established under suitable r-invexity assumption. Also lower bounds on the penalty parameter are given, for which above these values, this result is true.