Applied mathematics

Some properties of the support function of a convex set on a convex cone

L. N. Polyakova

St. Petersburg State University, Faculty of Applied Mathematics and Control Processes

Abstract: The concept of the support function of a convex set is one of the key ones in convex analysis. It was introduced by German mathematician H. Minkowski at the end of the 19th century. In this paper the properties of support functions on a closed convex cone are considered. For a convex compact set the concept of forming a set with respect to this cone is introduced. The properties of this set are studied. Conditions under which support functions of the two sets on the cone are equal are derived. Some drawings illustrate these properties.

Keywords: positively homogeneous convex function, support function, subdifferential of a convex function, conjugate cone.

UDC: 539.85


Accepted: April 26, 2012