A preconditioned difference of convex functions algorithm with extrapolation and line search
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910024106770432 |
|---|---|
| author | Zhang, Ran Sun, Hongpeng |
| author_facet | Zhang, Ran Sun, Hongpeng |
| contents | This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization problems. We introduce an adaptive conservative update strategy of the extrapolation parameter determined by a computationally efficient non-monotone line search. The core of our algorithm is to unite the update of the extrapolation parameter with the step size of the non-monotone line search interactively. The global convergence of the two proposed algorithms is established through the Kurdyka-Łojasiewicz properties, ensuring convergence within a preconditioned framework for linear equations. Numerical experiments on two general non-convex problems: SCAD-penalized binary classification and graph-based Ginzburg-Landau image segmentation models, demonstrate the proposed method's high efficiency compared to existing DC algorithms both in convergence rate and solution accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11914 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A preconditioned difference of convex functions algorithm with extrapolation and line search Zhang, Ran Sun, Hongpeng Optimization and Control Numerical Analysis 65K10, 65F08, 49K35, 90C25, 90C26 This paper proposes a novel proximal difference-of-convex (DC) algorithm enhanced with extrapolation and aggressive non-monotone line search for solving non-convex optimization problems. We introduce an adaptive conservative update strategy of the extrapolation parameter determined by a computationally efficient non-monotone line search. The core of our algorithm is to unite the update of the extrapolation parameter with the step size of the non-monotone line search interactively. The global convergence of the two proposed algorithms is established through the Kurdyka-Łojasiewicz properties, ensuring convergence within a preconditioned framework for linear equations. Numerical experiments on two general non-convex problems: SCAD-penalized binary classification and graph-based Ginzburg-Landau image segmentation models, demonstrate the proposed method's high efficiency compared to existing DC algorithms both in convergence rate and solution accuracy. |
| title | A preconditioned difference of convex functions algorithm with extrapolation and line search |
| topic | Optimization and Control Numerical Analysis 65K10, 65F08, 49K35, 90C25, 90C26 |
| url | https://arxiv.org/abs/2505.11914 |