Minimizing Compositions of Differences-of-Convex Functions with Smooth Mappings

• 成果类型: Article; Early Access
• 署名作者: Le Thi, Hoai An; Huynh, Van Ngai; Dinh, Tao Pham
• 署名单位: Universite de Lorraine; Institut Universitaire de France
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.0258
• 发表日期: 2023
• 关键词: Optimization; algorithm; nonsmooth; regularization; CONVERGENCE

摘要

We address the so-called DC (difference-of-convex functions) composite minimization problems (or DC composite programs) whose objective function is a composition of a DC function with a continuously differentiable mapping. We first develop an algorithm named DC composite algorithm (DCCA in short) for unconstrained DC composite programs and further extend to DC composite programs with constraints of inclusion associated with a smooth mapping and a closed convex set. The convergence analysis of the proposed algorithms is investigated. Applications of DCCA for two different problems, computation of the numerical radius of a square matrix and minimization of composite energies, are presented.