On some properties of quasi convex functions and sets

R. A. Khachatryan

Yerevan State University

Abstract: The connection between quasi convexity and proximal smoothness (also known as low $C^2$ property) of functions is verified. For compact sets, it is proved that the properties of quasi convexity and proximal smoothness are equivalent. The Bouligand cones of tangent directions for the sets that are defined by convex functions are constructed.

Keywords: multi-valued map, quasi convex set, star set, proximal smooth set, low $C^2$ property, tangent cone.

UDC: 519.6

Received: 19.04.2018

DOI: 10.20310/1810-0198-2018-23-124-824-837

Bibliographic databases:

•