A derivative-free nonmonotone line-search technique for unconstrained optimization

Authors:
M. A. Diniz-Ehrhardt;J. M. Martínez;M. Raydan
Affiliations:
Department of Applied Mathematics IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil;Department of Applied Mathematics IMECC-UNICAMP, University of Campinas, CP 6065, 13081-970 Campinas SP, Brazil;Departamento de Computación, Facultad de Ciencias, Universidad Central de Venezuela, Ap. 47002, Caracas 1041-A, Venezuela
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

A tolerant derivative-free nonmonotone line-search technique is proposed and analyzed. Several consecutive increases in the objective function and also nondescent directions are admitted for unconstrained minimization. To exemplify the power of this new line search we describe a direct search algorithm in which the directions are chosen randomly. The convergence properties of this random method rely exclusively on the line-search technique. We present numerical experiments, to illustrate the advantages of using a derivative-free nonmonotone globalization strategy, with approximated-gradient type methods and also with the inverse SR1 update that could produce nondescent directions. In all cases we use a local variation finite differences approximation to the gradient.