Primal-dual algorithm for weakly convex functions under sharpness conditions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917819335049216 |
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| author | Bednarczuk, Ewa Tran, The Hung Syga, Monika |
| author_facet | Bednarczuk, Ewa Tran, The Hung Syga, Monika |
| contents | We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap function. Under the sharpness condition of this new function, we identify the area around the set of saddle points where we obtain the convergence of the primal-dual algorithm. We give numerical examples and applications in image denoising and deblurring to demonstrate our results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_20977 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Primal-dual algorithm for weakly convex functions under sharpness conditions Bednarczuk, Ewa Tran, The Hung Syga, Monika Optimization and Control Numerical Analysis We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap function. Under the sharpness condition of this new function, we identify the area around the set of saddle points where we obtain the convergence of the primal-dual algorithm. We give numerical examples and applications in image denoising and deblurring to demonstrate our results. |
| title | Primal-dual algorithm for weakly convex functions under sharpness conditions |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2410.20977 |