New Bregman proximal type algorithms for solving DC optimization problems

Autor(es)

Takahashi, Shota ; Fukuda, Mituhiro ; Tanaka, Mirai

• Tipo de documento: Artigo Científico
• Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 83, n. 3, p. 39-pg., 2022-09-23.

Resumo

Difference of Convex (DC) optimization problems have objective functions that are differences between two convex functions. Representative ways of solving these problems are the proximal DC algorithms, which require that the convex part of the objective function have L-smoothness. In this article, we propose the Bregman Proximal DC Algorithm (BPDCA) for solving large-scale DC optimization problems that do not possess L-smoothness. Instead, it requires that the convex part of the objective function has the L-smooth adaptable property that is exploited in Bregman proximal gradient algorithms. In addition, we propose an accelerated version, the Bregman Proximal DC Algorithm with extrapolation (BPDCAe), with a new restart scheme. We show the global convergence of the iterates generated by BPDCA(e) to a limiting critical point under the assumption of the Kurdyka-Lojasiewicz property or subanalyticity of the objective function and other weaker conditions than those of the existing methods. We applied our algorithms to phase retrieval, which can be described both as a nonconvex optimization problem and as a DC optimization problem. Numerical experiments showed that BPDCAe outperformed existing Bregman proximal-type algorithms because the DC formulation allows for larger admissible step sizes. (AU)

• Processo FAPESP: 20/04585-7 - Desenvolvimento de métodos eficientes para problemas de otimização linear e não linear cônicas, e suas aplicações
• Beneficiário: Ernesto Julián Goldberg Birgin
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 18/24293-0 - Métodos computacionais de otimização
• Beneficiário: Sandra Augusta Santos
• Modalidade de apoio: Auxílio à Pesquisa - Temático