A Unified Zeroth-Order Proximal Newton-Type Framework for Composite Optimization
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866918487963729920 |
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| author | Liu, Zekun Fan, Jinyan |
| author_facet | Liu, Zekun Fan, Jinyan |
| contents | We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle complexity bounds for the algorithm to attain an $ε$-optimal solution under both nonconvex and strongly convex settings. We also establish its local R-superlinear convergence based on the Dennis--Moré condition, and theoretically address an open problem by showing that the BFGS scheme is more compatible with finite-difference gradient estimators than with smoothing-based ones. Numerical experiments are further presented to demonstrate the efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06016 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Zeroth-Order Proximal Newton-Type Framework for Composite Optimization Liu, Zekun Fan, Jinyan Optimization and Control 65K10, 90C30, 90C56, 90C53 We propose a unified derivative-free proximal Newton-type algorithm framework for solving composite optimization problems formulated as the sum of a black-box function and a known regularization term. We establish the iteration and oracle complexity bounds for the algorithm to attain an $ε$-optimal solution under both nonconvex and strongly convex settings. We also establish its local R-superlinear convergence based on the Dennis--Moré condition, and theoretically address an open problem by showing that the BFGS scheme is more compatible with finite-difference gradient estimators than with smoothing-based ones. Numerical experiments are further presented to demonstrate the efficiency of the proposed method. |
| title | A Unified Zeroth-Order Proximal Newton-Type Framework for Composite Optimization |
| topic | Optimization and Control 65K10, 90C30, 90C56, 90C53 |
| url | https://arxiv.org/abs/2605.06016 |