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Nonsmooth Calculus of Semismooth Functions and Maps

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  • Nooshin Movahedian

    (University of Isfahan)

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.

Suggested Citation

  • Nooshin Movahedian, 2014. "Nonsmooth Calculus of Semismooth Functions and Maps," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 415-438, February.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:2:d:10.1007_s10957-013-0407-4
    DOI: 10.1007/s10957-013-0407-4
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    References listed on IDEAS

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    1. Defeng Sun & Jie Sun, 2008. "Löwner's Operator and Spectral Functions in Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 33(2), pages 421-445, May.
    2. Jong-Shi Pang & Defeng Sun & Jie Sun, 2003. "Semismooth Homeomorphisms and Strong Stability of Semidefinite and Lorentz Complementarity Problems," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 39-63, February.
    3. Liqun Qi, 1993. "Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations," Mathematics of Operations Research, INFORMS, vol. 18(1), pages 227-244, February.
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