A derivative-free algorithm for nonlinear programming
نویسندگان
چکیده
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 exact penalty function; this approach shows two main difficulties: the first one is the nonsmoothness of this class of exact penalty functions; the second one is the fact that the equivalence between stationary points of the constrained problem and those of the exact penalty function can be stated only when the penalty parameter is smaller than a threshold value which is not known a priori. 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. In particular the proposed algorithm includes an updating rule for the penalty parameter which, after, at most, a finite number of updatings, is able to determine a “right value” of the penalty parameter. Numerical results on a set of test problems are reported which show the viability of the proposed algorithm. AMS subject classification. 65K05, 90C30, 90C56
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