Complexity of gradient descent for multiobjective optimization

• Autor(a) principal: Fliege, Jörg
• Data de Publicação: 2019
• Outros Autores: Vaz, António Ismael Freitas, Vicente, Luís Nunes
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• DOI: 10.1080/10556788.2018.1510928
• Texto Completo: http://hdl.handle.net/10316/89443; https://doi.org/10.1080/10556788.2018.1510928
• topic: Multiobjective optimization; gradient descent; steepest descent; global rates; worst-case complexity

A number of first-order methods have been proposed for smooth multiobjective optimization for which some form of convergence to first-order criticality has been proved. Such convergence is global in the sense of being independent of the starting point. In this paper, we analyse the rate of convergence of gradient descent for smooth unconstrained multiobjective optimization, and we do it for non-convex, convex, and strongly convex vector functions. These global rates are shown to be the same as for gradient descent in single-objective optimization and correspond to appropriate worst-case complexity bounds. In the convex cases, the rates are given for implicit scalarizations of the problem vector function.