An Inexact Proximal Newton Method for Nonconvex Composite Minimization

Hong Zhu

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arXiv · 2412.16535

An Inexact Proximal Newton Method for Nonconvex Composite Minimization

Hong Zhu

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Abstract

In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order $\mathcal{O}(k^{-1/2})$ in terms of the minimal norm of the KKT residual mapping and the local superlinear convergence rate in terms of the sequence generated by the proposed algorithm under the higher-order metric $q$-subregularity property. When the Lipschitz constant of the corresponding gradient is known, we show that the proposed algorithm is well-defined without line search. Extensive numerical experiments on the $\ell_1$-regularized Student's $t$-regression and the group penalized Student's $t$-regression show that the performance of the proposed method is comparable to the state-of-the-art proximal Newton-type methods.

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BibTeX RIS

Hong Zhu. 2024-12-21. An Inexact Proximal Newton Method for Nonconvex Composite Minimization. https://arxiv.org/abs/2412.16535

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