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 |
Files in This Item:
File | Size | Format | |
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bookPart_65503.pdf | 433,57 kB | Adobe PDF | View/Open |
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