Subdifferential characterization of s-lower regular functions

Abstract

As for Moreau envelopes of primal lower nice as well as prox-regular functions, Moreau s-envelopes of s-lower regular functions have been proved recently to have several remarkable differential properties and to have many important applications. Here, we provide a subdifferential characterization of extended real-valued s-lower regular functions on Banach spaces in terms of a hypomonotonicity-like property of the subdifferential.

Keywords:

• subdifferential
• s-lower regular function
• convexly composite function
• primal lower nice function
• hypomonotonicity

AMS Subject Classifications:

• Primary 49J52
• 58C06
• 58C2
• Secondary 90C30