A Derative-free algorithm for nonlinear programming

In this paper we consider nonlinear constrained optimization problems in case where the first order derivatives of the objective function and the constraints can not be used. Up to date only a few approaches have been proposed for tackling such a class of problems. In this work we propose a new algorithm. The starting point of the proposed approach is the possibility to transform the original constrained problem into an unconstrained or linearly constrained minimization of a nonsmooth ex-act penalty function. In this paper we propose a derivative-free algorithm which overcomes the preceding difficulties and produces a sequence of points that admits a subsequence converging towards Karush-Kuhn-Tucker points of the constrained problem. Numerical results on a set of test problems are reported which show the viability of the proposed algorithm. Giampaolo Liuzzi è docente presso la Facoltà di Ingegneria della “Sapienza” Università di Roma.Stefano Lucidi è docente presso la Facoltà di Ingegneria della “Sapienza” Università di Roma.