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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.02084 |
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| _version_ | 1866911356228206592 |
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| author | Feng, Zhangcheng Yuan, Yancheng |
| author_facet | Feng, Zhangcheng Yuan, Yancheng |
| contents | This paper introduces an efficient perturbed difference-of-convex algorithm (pDCA) for computing d-stationary points of an important class of structured nonsmooth difference-of-convex problems. Compared to the principal algorithms introduced in [J.-S. Pang, M. Razaviyayn, and A. Alvarado, Math. Oper. Res. 42(1):95--118 (2017)], which may require solving several subproblems for a one-step update, pDCA only requires solving a single subproblem. Therefore, the computational cost of pDCA for one-step update is comparable to the widely used difference-of-convex algorithm (DCA) introduced in [D. T. Pham and H. A. Le Thi, Acta Math. Vietnam. 22(1):289--355 (1997)] for computing a critical point. Importantly, under practical assumptions, we prove that every accumulation point of the sequence generated by pDCA is a d-stationary point almost surely. Numerical experiment results on several important examples of nonsmooth DC programs demonstrate the efficiency of pDCA for computing d-stationary points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02084 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Perturbed DCA for Computing d-Stationary Points of Nonsmooth DC Programs Feng, Zhangcheng Yuan, Yancheng Optimization and Control This paper introduces an efficient perturbed difference-of-convex algorithm (pDCA) for computing d-stationary points of an important class of structured nonsmooth difference-of-convex problems. Compared to the principal algorithms introduced in [J.-S. Pang, M. Razaviyayn, and A. Alvarado, Math. Oper. Res. 42(1):95--118 (2017)], which may require solving several subproblems for a one-step update, pDCA only requires solving a single subproblem. Therefore, the computational cost of pDCA for one-step update is comparable to the widely used difference-of-convex algorithm (DCA) introduced in [D. T. Pham and H. A. Le Thi, Acta Math. Vietnam. 22(1):289--355 (1997)] for computing a critical point. Importantly, under practical assumptions, we prove that every accumulation point of the sequence generated by pDCA is a d-stationary point almost surely. Numerical experiment results on several important examples of nonsmooth DC programs demonstrate the efficiency of pDCA for computing d-stationary points. |
| title | A Perturbed DCA for Computing d-Stationary Points of Nonsmooth DC Programs |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2601.02084 |