A DIRECT SEARCH QUASI-NEWTON METHOD FOR NONSMOOTH UNCONSTRAINED OPTIMIZATION. (23rd October 2017)

• Record Type: Journal Article
• Authors: PRICE, C. J.
• Is Part Of: ANZIAM journal. Volume 59:Number 2(2017)
• Page Start: 215
• Page End: 231
• Publication Date: 2017-10-23
• Subjects: 65K05; derivative free, -- nonconvex, -- Clarke generalized derivative; 510.5
• DOI: 10.1017/S1446181117000323
• Languages: English
• ISSNs: 1446-1811

Abstract

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.