Paper Info
Title
A Derivative-Free Algorithm for Inequality Constrained Nonlinear Programming via Smoothing of an linfty Penalty Function
Abstract
In this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used. Our starting point 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 which may cause derivative-free codes to converge to nonstationary points of the problem; the second one is the fact that the equivalence between stationary points of the constrained problem and those of the exact penalty function can only be stated 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 to a Karush-Kuhn-Tucker point of the constrained problem. In particular the proposed algorithm is based on a smoothing of the nondifferentiable exact penalty function and includes an updating rule which, after at most a finite number of updates, is able to determine a "right value" for the penalty parameter. Furthermore we present the results obtained on a real world problem concerning the estimation of parameters in an insulin-glucose model of the human body.
Year
DOI
Venue
2009
10.1137/070711451
SIAM JOURNAL ON OPTIMIZATION
Keywords
DocType
Volume
derivative-free optimization,constrained optimization,nonlinear programming,nondifferentiable exact penalty functions
Journal
20
Issue
ISSN
Citations 
1
1052-6234
1
PageRank 
References 
Authors
0.40
5
2
Name
Order
Citations
PageRank
G. Liuzzi119517.16
Stefano Lucidi278578.11