ANALISIS MASALAH EKSTREM FUNGSI PADA RUANG BERNORMA

Abstract

In this thesis, we discuss about a point which minimize the value of a function on normed space in analysis. At first, we introduce the convex sets and the convex functions on normed space. The discussion in the convex set and the convex function including the definition and basic properties of them. Furthermore, we discuss the function that has lower semi-continuous from above, the Legendre-Fenchel transform and subdifferentials of convex functions, and the constraint of extreme functions, and we shall prove the Ekeland Variational Principle and the Borwein-Preiss Smooth Variational Principle