Convex Programming Based on Hahn-Banach Theorem

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Convex Programming Based on Hahn-Banach Theorem

January 6, 2020 MATHEMATICS Science 0

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.

For more information contact author

Manuel Alberto M. Ferreira
ISTAR-IUL – Information Sciences, Technologies and Architecture Research Center (ISTA), Portugal.
E-mail: [email protected], [email protected]

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