Nonsmooth Calculus of Semismooth Functions and Maps

Nooshin Movahedian ()
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Nooshin Movahedian: University of Isfahan

Journal of Optimization Theory and Applications, 2014, vol. 160, issue 2, No 3, 415-438

Abstract: Abstract 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.

Keywords: Semismooth set; Semismooth function; Semismooth map; Nonsmooth analysis; Normal cone; Subdifferential; Coderivative (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0407-4

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