Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916415067389952 |
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| author | Pham, Tan Nhat Dao, Minh N. Eberhard, Andrew Sultanova, Nargiz |
| author_facet | Pham, Tan Nhat Dao, Minh N. Eberhard, Andrew Sultanova, Nargiz |
| contents | In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka--Lojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02635 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions Pham, Tan Nhat Dao, Minh N. Eberhard, Andrew Sultanova, Nargiz Optimization and Control 90C26, 49M27, 65K05 In this paper, we develop a splitting algorithm incorporating Bregman distances to solve a broad class of linearly constrained composite optimization problems, whose objective function is the separable sum of possibly nonconvex nonsmooth functions and a smooth function, coupled by a difference of functions. This structure encapsulates numerous significant nonconvex and nonsmooth optimization problems in the current literature including the linearly constrained difference-of-convex problems. Relying on the successive linearization and alternating direction method of multipliers (ADMM), the proposed algorithm exhibits the global subsequential convergence to a stationary point of the underlying problem. We also establish the convergence of the full sequence generated by our algorithm under the Kurdyka--Lojasiewicz property and some mild assumptions. The efficiency of the proposed algorithm is tested on a robust principal component analysis problem and a nonconvex optimal power flow problem. |
| title | Bregman Proximal Linearized ADMM for Minimizing Separable Sums Coupled by a Difference of Functions |
| topic | Optimization and Control 90C26, 49M27, 65K05 |
| url | https://arxiv.org/abs/2401.02635 |