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Ferreira, M. A. M. (2020). Convex programming based on Hahn Banach theorem. In Luigi Giacomo Rodino (Ed.), Theory and Applications of Mathematical Science. (pp. 60-72). Hooghly: Book Publisher International.
M. A. Ferreira, " Convex programming based on Hahn Banach theorem", in Theory and Applications of Mathematical Science, Luigi Giacomo Rodino, Ed., Hooghly, Book Publisher International, 2020, vol. 1, pp. 60-72
@incollection{ferreira2020_1716179631039, author = "Ferreira, M. A. M.", title = " Convex programming based on Hahn Banach theorem", chapter = "", booktitle = "Theory and Applications of Mathematical Science", year = "2020", volume = "1", series = "", edition = "1", pages = "60-60", publisher = "Book Publisher International", address = "Hooghly", url = "http://www.bookpi.org/bookstore/product/theory-and-applications-of-mathematical-science/" }
TY - CHAP TI - Convex programming based on Hahn Banach theorem T2 - Theory and Applications of Mathematical Science VL - 1 AU - Ferreira, M. A. M. PY - 2020 SP - 60-72 DO - : 10.9734/bpi/tams/v1 CY - Hooghly UR - http://www.bookpi.org/bookstore/product/theory-and-applications-of-mathematical-science/ AB - 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. ER -