From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

Robert Baier (), Elza Farkhi () and Vera Roshchina ()
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Robert Baier: University of Bayreuth
Elza Farkhi: Tel Aviv University
Vera Roshchina: RMIT University

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 4, 384-401

Abstract: Abstract We derive exact calculus rules for the directed subdifferential defined for the class of directed subdifferentiable functions. We also state optimality conditions, a chain rule and a mean-value theorem. Thus, we extend the theory of the directed subdifferential from quasidifferentiable to directed subdifferentiable functions.

Keywords: Nonconvex subdifferentials; Directional derivatives; Difference of convex (DC) functions; Mean-value theorem and chain rule for nonsmooth functions; 49J52; 90C26; 26B25; 58C20 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-016-0926-x

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