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A Derivative-Free Algorithm for Constrained Global Optimization based on Exact Penalty Functions

G. Di Pillo(dipillo***at***dis.uniroma1.it)
S. Lucidi(lucidi***at***dis.uniroma1.it)
F. Rinaldi(rinaldi***at***math.unipd.it)

Abstract: Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization technique for minimizing a non-differentiable exact penalty func- tion for given values of the penalty parameter, and an automatic updating of the penalty parameter that occurs only a finite number of times. However, in the updating of the penalty parameter, the method requires the evaluation of the derivatives of the problem functions. In this work, we show that an efficient updating can be implemented also without using the problem derivatives, in this way making the approach suitable for globally solving constrained prob- lems where the derivatives are not available. In the algorithm, any efficient derivative-free unconstrained global minimization technique can be used. In particular, we adopt an improved version of the DIRECT algorithm. In ad- dition, to improve the performances, the approach is enriched by resorting to derivative-free local searches, in a multistart framework. In this context, we prove that, under suitable assumptions, for every global minimum point there exists a neighborhood of attraction for the local search. An extensive numerical experience is reported.

Keywords: Nonlinear Optimization · Global Optimization · Exact Penalty Functions · Derivative-Free Minimization · DIRECT Algorithm

Category 1: Nonlinear Optimization

Category 2: Global Optimization

Citation: Journal of Optimization Theory and Applications (to appear)

Download: [PDF]

Entry Submitted: 11/14/2013
Entry Accepted: 11/14/2013
Entry Last Modified: 11/14/2013

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