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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Vydáno v:The ANZIAM journal Ročník 59; číslo 2; s. 215 - 231
Hlavní autor: PRICE, C. J.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Cambridge, UK Cambridge University Press 01.10.2017
Témata:
Algorithms
Estimates
Methods
Optimization
Quasi Newton methods
65K05
nonconvex
Clarke generalized derivative
derivative free
ISSN:1446-1811, 1446-8735
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Abstract 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.
AbstractList 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.
Author PRICE, C. J.
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  surname: PRICE
  fullname: PRICE, C. J.
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  organization: Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand email C.Price@math.canterbury.ac.nz
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CitedBy_id crossref_primary_10_1080_10556788_2020_1746961
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nonconvex
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Snippet A direct search quasi-Newton algorithm is presented for local minimization of Lipschitz continuous black-box functions. The method estimates the gradient via...
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SubjectTerms Algorithms
Estimates
Methods
Optimization
Quasi Newton methods
Title A DIRECT SEARCH QUASI-NEWTON METHOD FOR NONSMOOTH UNCONSTRAINED OPTIMIZATION
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