Inexact proximal DC Newton-type method for nonconvex composite functions

Shummin Nakayama (), Yasushi Narushima () and Hiroshi Yabe ()
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Shummin Nakayama: The University of Electro-Communications
Yasushi Narushima: Keio University
Hiroshi Yabe: Tokyo University of Science

Computational Optimization and Applications, 2024, vol. 87, issue 2, No 10, 640 pages

Abstract: Abstract We consider a class of difference-of-convex (DC) optimization problems where the objective function is the sum of a smooth function and a possibly nonsmooth DC function. The application of proximal DC algorithms to address this problem class is well-known. In this paper, we combine a proximal DC algorithm with an inexact proximal Newton-type method to propose an inexact proximal DC Newton-type method. We demonstrate global convergence properties of the proposed method. In addition, we give a memoryless quasi-Newton matrix for scaled proximal mappings and consider a two-dimensional system of semi-smooth equations that arise in calculating scaled proximal mappings. To efficiently obtain the scaled proximal mappings, we adopt a semi-smooth Newton method to inexactly solve the system. Finally, we present some numerical experiments to investigate the efficiency of the proposed method, which show that the proposed method outperforms existing methods.

Keywords: Nonsmooth optimization; Proximal DC algorithm; Inexact proximal Newton-type method; Memoryless quasi-Newton method; Semi-smooth Newton method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10589-023-00525-9

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