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From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules

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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.

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Acknowledgments

We thank Wolfgang Achtziger for motivating us to study the mean-value theorem. This work was partially supported by The Hermann Minkowski Center for Geometry at Tel Aviv University, Tel Aviv, Israel.

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Authors and Affiliations

  1. Chair of Applied Mathematics, University of Bayreuth, 95440, Bayreuth, Germany

    Robert Baier

  2. School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Elza Farkhi

  3. School of Science, RMIT University, Melbourne, VIC, 3001, Australia

    Vera Roshchina

Authors
  1. Robert Baier
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  2. Elza Farkhi
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  3. Vera Roshchina
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Correspondence to Robert Baier.

Additional information

Elza Farkhi: On leave from the Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences.

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Baier, R., Farkhi, E. & Roshchina, V. From Quasidifferentiable to Directed Subdifferentiable Functions: Exact Calculus Rules. J Optim Theory Appl 171, 384–401 (2016). https://doi.org/10.1007/s10957-016-0926-x

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  • DOI: https://doi.org/10.1007/s10957-016-0926-x

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