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Convex Programming Based on Hahn-Banach Theorem
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Convex Programming Based on Hahn-Banach Theorem | Chapter 05 | Theory and Applications of Mathematical Science Vol. 1
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.
Author(s) Details
Manuel Alberto M. Ferreira
ISTAR-IUL - Information Sciences, Technologies and Architecture Research Center (ISTA), Portugal.
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.
Author(s) Details
Manuel Alberto M. Ferreira
ISTAR-IUL - Information Sciences, Technologies and Architecture Research Center (ISTA), Portugal.
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