Inexact proximal DC Newton-type method for nonconvex composite functions

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 alg...

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Bibliographic Details
Published in:Computational optimization and applications Vol. 87; no. 2; pp. 611 - 640
Main Authors: Nakayama, Shummin, Narushima, Yasushi, Yabe, Hiroshi
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2024
Springer Nature B.V
Subjects:
Algorithms
Approximation
Composite functions
Convex and Discrete Geometry
Efficiency
Machine learning
Management Science
Mathematics
Mathematics and Statistics
Methods
Newton methods
Numerical analysis
Operations Research
Operations Research/Decision Theory
Optimization
Statistics
Memoryless quasi-Newton method
Proximal DC algorithm
Nonsmooth optimization
Semi-smooth Newton method
Inexact proximal Newton-type method
ISSN:0926-6003, 1573-2894
Online Access:Get full text
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Summary: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.
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ISSN:0926-6003
1573-2894
DOI:10.1007/s10589-023-00525-9