Nonsmooth Calculus of Semismooth Functions and Maps

作者：Movahedian Nooshin^*

来源：Journal of Optimization Theory and Applications, 2014, 160(2): 415-438.

DOI：10.1007/s10957-013-0407-4

• Semismooth set
• Semismooth function
• Semismooth map
• Nonsmooth analysis
• Normal cone
• Subdifferential
• Coderivative

In this paper, we pursue two goals. First, we find exact relationships between the three concepts of semismooth sets, functions, and maps. Then, we consider the nonsmooth calculus of these notions. Particularly, we prove that the Mordukhovich and linear subdifferentials (coderivatives) are equal for the semismooth functions (maps). Several examples are presented to illustrate the results of the paper.

• 出版日期2014-2