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arXiv · 2111.07618

Inexact proximal DC Newton-type method for nonconvex composite functions

Shummin Nakayama·Yasushi Narushima·Hiroshi Yabe
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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 possible 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, showing that the proposed method outperforms existing methods.

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Shummin Nakayama, Yasushi Narushima, Hiroshi Yabe. 2021-11-15. Inexact proximal DC Newton-type method for nonconvex composite functions. https://arxiv.org/abs/2111.07618

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