Método do ponto proximal inexato para minimização quase-convexa em variedades de Hadamard
type: CreativeWork
description: In this thesis, we present an inexact proximal point algorithm to solve quasiconvex optimization problems in Riemannian manifolds with non positive sectional curvature, called Hadamard manifolds. Then, we show that under mild hypotheses on the optimization problem, the sequence generated by the proposed method are well defined and converge to critical points of the problem. We also prove that the convergence rate of the ones is linear and superlinear in some cases. Furthermore, by focusing on the importance of applications in economics and localization theory, we extend the proposed algorithm for solving multiobjective quasiconvex optimization problem. Moreover, convergencia of the sequence to a Pareto-Clarke critical point is obtained assuming reasonable hypotheses. Finally, computational experiments were done to validate the proposed model and results found.
abstract: In this thesis, we present an inexact proximal point algorithm to solve quasiconvex optimization problems in Riemannian manifolds with non positive sectional curvature, called Hadamard manifolds. Then, we show that under mild hypotheses on the optimization problem, the sequence generated by the proposed method are well defined and converge to critical points of the problem. We also prove that the convergence rate of the ones is linear and superlinear in some cases. Furthermore, by focusing on the importance of applications in economics and localization theory, we extend the proposed algorithm for solving multiobjective quasiconvex optimization problem. Moreover, convergencia of the sequence to a Pareto-Clarke critical point is obtained assuming reasonable hypotheses. Finally, computational experiments were done to validate the proposed model and results found.
author: Cusihuallpa, Nancy Baygorrea
language: por
keywords: Engenharia de Sistemas e Computação, Método do ponto proximal, Variedades de Hadamard
date published: 2017-02
date modified: 2026-07-24T01:16:29Z
provider: Brazil UERJ
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Universidade Federal do Rio de Janeiro

PropertyValue
property ID: Handle
value: http://hdl.handle.net/11422/8174