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A DIRECT SEARCH QUASI-NEWTON METHOD FOR NONSMOOTH UNCONSTRAINED OPTIMIZATION

Published online by Cambridge University Press:  23 October 2017

C. J. PRICE Open the ORCID record for C. J. PRICE [Opens in a new window]
C. J. PRICE*
Affiliation:
Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand email C.Price@math.canterbury.ac.nz
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Abstract

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A direct search quasi-Newton algorithm is presented for local minimization of Lipschitz continuous black-box functions. The method estimates the gradient via central differences using a maximal frame around each iterate. When nonsmoothness prevents progress, a global direction search is used to locate a descent direction. Almost sure convergence to Clarke stationary point(s) is shown, where convergence is independent of the accuracy of the gradient estimates. Numerical results show that the method is effective in practice.

Keywords

derivative freenonconvexClarke generalized derivative

MSC classification

Primary: 65K05: Mathematical programming methods
Type
Research Article
Information
The ANZIAM Journal , Volume 59 , Issue 2 , October 2017 , pp. 215 - 231
Copyright
© 2017 Australian Mathematical Society 

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