Kuhn-Tucker’s theorem: The fundamental result in convex programming applied to finance and economic sciences

Abstract

The optimization problems are not so important now in the field of production. But in the minimization risk problems, in profits maximization problems, in Marketing Research, in Finance, they are completely actual. An important example is the problem of minimizing portfolio risk, demanding a certain mean return. The main mathematical tool to solve these problems is the convex programming and the main result is the Kuhn-Tucker Theorem. In this work that result mathematical fundaments, in the context of real Hilbert spaces, are presented.