A DIRECT SEARCH QUASI-NEWTON METHOD FOR NONSMOOTH UNCONSTRAINED OPTIMIZATION

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 loca...

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Bibliographic Details
Published in:The ANZIAM journal Vol. 59; no. 2; pp. 215 - 231
Main Author: PRICE, C. J.
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.10.2017
Subjects:
Algorithms
Estimates
Methods
Optimization
Quasi Newton methods
65K05
nonconvex
Clarke generalized derivative
derivative free
ISSN:1446-1811, 1446-8735
Online Access:Get full text
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Summary: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.
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ISSN:1446-1811
1446-8735
DOI:10.1017/S1446181117000323