## Convex Programming Based on Hahn-Banach Theorem

*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]

**View Books: **http://bp.bookpi.org/index.php/bpi/catalog/book/117

Books convex programming Hahn-Banach theorem Kuhn-Tucker theorem minimax theorem. Science separation theorems