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The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus

Abstract : We continue the study of the directed subdifferential for quasidifferentiable functions started in [R. Baier, E. Farkhi, V. Roshchina, The directed and Rubinov subdifferentials of quasidifferentiable functions, Part I: Definition and examples (this journal)]. Calculus rules for the directed subdifferentials of sum, product, quotient, maximum and minimum of quasidifferentiable functions are derived. The relation between the Rubinov subdifferential and the subdifferentials of Clarke, Dini, Michel-Penot, and Mordukhovich is discussed. Important properties implying the claims of Ioffe's axioms as well as necessary and sufficient optimality conditions for the directed subdifferential are obtained.
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https://hal.inria.fr/hal-00724863
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Submitted on : Wednesday, August 22, 2012 - 7:13:08 PM
Last modification on : Friday, October 13, 2017 - 5:08:16 PM

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Robert Baier, Elza Farkhi, Vera Roshchina. The directed and Rubinov subdifferentials of quasidifferentiable functions, Part II: Calculus. Nonlinear Analysis: Theory, Methods and Applications, Elsevier, 2012, 75 (3), pp.1058-1073. ⟨10.1016/j.na.2011.04.073⟩. ⟨hal-00724863⟩

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