Método de Newton para encontrar zeros de uma classe especial de funções semi-suaves

• Autor(a) principal: Louzeiro, Mauricio Silva
• Data de Publicação: 2016
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000007v68
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/5724
• topic: Método de Newton; Equação semi-suave; Cone simplicial; Função quadr atica; Newton's method; Semi-smooth equation; Simplicial cone; Quadratic function; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we will study a new strategy to minimize a convex function on a simplicial cone. This method consists in to obtain the solution of a minimization problem through the root of a semi-smooth equation associated to its optimality conditions. To nd this root, we use the semi-smooth version of the Newton's method, where the derivative of the function that de nes the semi-smooth equation is replaced by a convenient Clarke subgradient. For the case that the function is quadratic, we will see that it allows us to have weaker conditions for the convergence of the sequence generated by the semi-smooth Newton's method. Motivated by this new minimization strategy we will also use the semi-smooth Newton's method to nd roots of two special semi-smooth equations, one associated to x+ and the another one associated to jxj.