The exact absolute value penalty function method for identifying strict global minima of order m in nonconvex nonsmooth programming

Abstract

In this paper, it is demonstrated that the exact absolute value penalty function method is useful for identifying the special sort of minimizers in nonconvex nonsmooth optimization problems with both inequality and equality constraints. The equivalence between the sets of strict global minima of order m in nonsmooth minimization problem and of its associated penalized optimization problem with the exact l1penalty function is established under nondifferentiable (F, ρ) -convexity assumptions imposed on the involved functions. The threshold of the penalty parameter, above which this result holds, is also given.