String-averaging incremental subgradient methods for constrained convex optimization problems

• Ano de defesa: 2017
• Autor(a) principal: Oliveira, Rafael Massambone de
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Algoritmos de média das sequências; Convex optimization; Incremental subgradient methods; Métodos de subgradientes incrementais; Otimização convexa; Otimização estocástica; Stochastic optimization; String-averaging algorithms
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/55/55134/tde-14112017-150512/

In this doctoral thesis, we propose new iterative methods for solving a class of convex optimization problems. In general, we consider problems in which the objective function is composed of a finite sum of convex functions and the set of constraints is, at least, convex and closed. The iterative methods we propose are basically designed through the combination of incremental subgradient methods and string-averaging algorithms. Furthermore, in order to obtain methods able to solve optimization problems with many constraints (and possibly in high dimensions), generally given by convex functions, our analysis includes an operator that calculates approximate projections onto the feasible set, instead of the Euclidean projection. This feature is employed in the two methods we propose; one deterministic and the other stochastic. A convergence analysis is proposed for both methods and numerical experiments are performed in order to verify their applicability, especially in large scale problems.