Alternating DC algorithm for partial DC programming problems
| Autor: | Van Ngai Huynh, Hoai An Le Thi, Tao Pham Dinh, Vinh Thanh Ho |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), Department of Mathematics, University of Quynhon, 170 An Duong Vuong, Qui Nhon, Vietnam, Laboratoire de Génie Informatique, de Production et de Maintenance (LGIPM), Université de Lorraine (UL) |
| Rok vydání: | 2021 |
| Předmět: |
021103 operations research
Control and Optimization Intersection (set theory) Applied Mathematics 0211 other engineering and technologies 010103 numerical & computational mathematics 02 engineering and technology Management Science and Operations Research 01 natural sciences Critical point (mathematics) Computer Science Applications Convergence (routing) [INFO]Computer Science [cs] Point (geometry) [MATH]Mathematics [math] 0101 mathematics Convex function Algorithm Robust principal component analysis ComputingMilieux_MISCELLANEOUS Dykstra's projection algorithm Mathematics Variable (mathematics) |
| Zdroj: | Journal of Global Optimization Journal of Global Optimization, Springer Verlag, In press, ⟨10.1007/s10898-021-01043-w⟩ |
| ISSN: | 1573-2916 0925-5001 |
| DOI: | 10.1007/s10898-021-01043-w |
| Popis: | DC (Difference of Convex functions) programming and DCA (DC Algorithm) play a key role in nonconvex programming framework. These tools have a rich and successful history of thirty five years of development, and the research in recent years is being increasingly explored to new trends in the development of DCA: design novel DCA variants to improve standard DCA, to deal with the scalability and with broader classes than DC programs. Following these trends, we address in this paper the two wide classes of nonconvex problems, called partial DC programs and generalized partial DC programs, and investigate an alternating approach based on DCA for them. A partial DC program in two variables $$(x,y)\in \mathbb {R}^{n}\times {\mathbb {R}}^{m}$$ takes the form of a standard DC program in each variable while fixing other variable. A so-named alternating DCA and its inexact/generalized versions are developed. The convergence properties of these algorithms are established: both exact and inexact alternating DCA converge to a weak critical point of the considered problem, in particular, when the Kurdyka–Łojasiewicz inequality property is satisfied, the algorithms furnish a Frechet/Clarke critical point. The proposed algorithms are implemented on the problem of finding an intersection point of two nonconvex sets. Numerical experiments are performed on an important application that is robust principal component analysis. Numerical results show the efficiency and the superiority of the alternating DCA comparing with the standard DCA as well as a well known alternating projection algorithm. |
| Databáze: | OpenAIRE |
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