Sobre a convergência de métodos de descida em otimização não-suave: aplicações à ciência comportamental

• Autor(a) principal: Sousa Júnior, Valdinês Leite de
• Data de Publicação: 2017
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000004cbw
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6864
• topic: Métodos de descida; Propriedade Kurdyka-Lojasiewicz; Otimização multiobjetivo; Ciência comportamental; Racionalidade variacional; Método do ponto proximal; Descent methods; Kurdyka-Lojasiewicz property; Multiobjective optimization; Behavioral sciences; Variational rationality; Proximal point method; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we investigate four different types of descent methods: a dual descent method in the scalar context and a multiobjective proximal point methods (one exact and two inexact versions). The first one is restricted to functions that satisfy the Kurdyka-Lojasiewicz property, where it is used a quasi-distance as a regularization function. In the next three methods, the objective is to study the convergence of a multiobjective proximal methods (exact an inexact) for a particular class of multiobjective functions that are not necessarily differentiable. For the inexact methods, we choose a proximal distance as the regularization term. Such a well-known distance allows us to analyze the convergence of the method under various settings. Applications in behavioral sciences are analyzed in the sense of the variational rationality approach.