Espaços vetoriais e topológicos de intervalos generalizados com alguns conceitos de cálculo e otimização intervalar

This work presents a method to endow the generalized interval set M = I(R) ∪ I(R); where I(R) = f[a1; a2] : a1 a2 and a1; a2 2 Rg and I(R) = f[a1; a2] : [a2; a1] 2 I(R)g; with some different structures, such as algebraic, topological, and metric. We also equip M with order relations. Actually, we di...

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Bibliographic Details
Author: Costa, Tiago Mendonça da [UNESP]
Format: doctoral thesis
Status:Published version
Publication Date:2014
Country:Brasil
Institution:Universidade Estadual Paulista (UNESP)
Repository:Repositório Institucional da UNESP
Language:Portuguese
OAI Identifier:oai:repositorio.unesp.br:11449/110603
Online Access:http://hdl.handle.net/11449/110603
Access Level:Open access
Keyword:Álgebra linear
Espaços topologicos
Espaços vetoriais
Otimização matematica
Topological spaces
Description
Summary:This work presents a method to endow the generalized interval set M = I(R) ∪ I(R); where I(R) = f[a1; a2] : a1 a2 and a1; a2 2 Rg and I(R) = f[a1; a2] : [a2; a1] 2 I(R)g; with some different structures, such as algebraic, topological, and metric. We also equip M with order relations. Actually, we did this in a more general context because we worked in Mn = M M M for n 2 N: We formulated interval optimization problems and related them to classic multi-objective optimization problems. We presented a version of the mini-max Theorem in the interval context, and also developed concepts of calculus on the generalized interval space which are used to find the attainable state set of a classic differential inclusion under some given conditions