Please use this identifier to cite or link to this item:
http://hdl.handle.net/10071/26471
Author(s): | Ferreira, M. A. M. |
Editor: | Le Bin Ho |
Date: | 2020 |
Title: | Some considerations on orthogonality, strict separation theorems and applications in Hilbert spaces |
Book title/volume: | Hilbert spaces: Properties and applications |
Pages: | 1 - 19 |
Collection title and number: | Mathematics research developments; |
Reference: | Ferreira, M. A. M. (2020). Some considerations on orthogonality, strict separation theorems and applications in Hilbert spaces. EM Le Bin Ho (Ed.). Hilbert spaces: Properties and applications (pp.1-19). Nova Science Publishers. http://hdl.handle.net/10071/26471 |
ISBN: | 978-1-53616-643-9 |
Keywords: | Hilbert spaces Convex sets Projections Orthogonality Riesz representation theorem Kuhn-Tucker theorem Minimax theorem |
Abstract: | After presenting some structural notions on Hilbert spaces, which constitute fundamental support for this work, we approach the goals of thechapter. First,studyaboutconvexsets,projections,andorthogonality, whereweapproachtheoptimizationprobleminHilbertspaceswithsome generality. Then the approach to Riesz representation theorem in this field, important in the rephrasing of the separation theorems. Then we give a look to the strict separation theorems as well as to the main results of convex programming: Kuhn-Tucker theorem and minimax theorem. These theorems are very important in the applications. Moreover, the presented strict separation theorems and the Riesz representation theorem have key importance in the demonstrations of Kuhn-Tucker and minimax theorems and respective corollaries. |
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_61529.pdf | 313,84 kB | Adobe PDF | View/Open |
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