THE l1 PENALTY FUNCTION METHOD FOR NONCONVEX DIFFERENTIABLE OPTIMIZATION PROBLEMS WITH INEQUALITY CONSTRAINTS

Abstract

In this paper, some new results on the l1 exact penalty function method are presented. A simple optimality characterization is given for the nonconvex differentiable optimization problems with inequality constraints via the l1 exact penalty function method. The equivalence between sets of optimal solutions in the original mathematical programming problem and its associated exact penalized optimization problem is established under suitable r-invexity assumption. The penalty parameter is given, above which this equivalence holds. Furthermore, the equivalence between a saddle point in the considered nonconvex mathematical programming problem with inequality constraints and a minimizer in its penalized optimization problem with the l1 exact penalty function is also established.