Seperability of Star-Shaped Sets and its Application to an Optimization Problem

Abstract

In this paper we deal with a separation problem of stat-shaped sets. It is shown that under natural assumptions two star-shaped subsets of n-dimensional Euclidean space R ⁿcan be separated by a finite set of linear functionals. The number of this functionals is determined by the dimension of the space R ⁿ The separation theorem for star-shaped sets is used in studying of global minimum conditions

Keywords:

• Separation Theorem
• Star-Shaped Sets
• Support Sets
• Global Minimum Conditions