Please use this identifier to cite or link to this item: http://hdl.handle.net/10071/26452
Author(s): Ferreira, M. A. M.
Editor: Luigi Giacomo Rodino
Date: 2020
Title: Convex programming based on Hahn Banach theorem
Volume: 1
Book title/volume: Theory and applications of mathematical science
Pages: 60 - 72
Reference: Ferreira, M. A. M. (2020). Convex programming based on Hahn Banach theorem. EM Luigi Giacomo Rodino (Ed.). Theory and applications of mathematical science (pp.60-72). Book Publisher International. 10.9734/bpi/tams/v1
ISBN: 978-93-89562-13-2
DOI (Digital Object Identifier): 10.9734/bpi/tams/v1
Keywords: Hahn-Banach theorem
Separation theorems
Convex programming
Kuhn-Tucker theorem
Minimax theorem
Abstract: The main objective of this chapter is to present the separation theorems, important consequences of Hahn-Theorem theorem. Therefore, we begin with an overview on convex sets and convex functionals. Then go on with the Hahn-Banach theorem and separation theorems. Follow these results specification: first for normed spaces and then for a subclass of these spaces, the Hilbert spaces. In this last case plays a key role the Riesz representation theorem. Separation theorems are key results in convex programming. Then the chapter ends with the outline of applications of these results in convex programming, Kuhn-Tucker theorem, and in minimax theorem, two important tools in operations research, management and economics,for instance.
Peerreviewed: yes
Access type: Open Access
Appears in Collections:ISTAR-CLI - Capítulos de livros internacionais

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