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Value Functions and Their Directional Derivatives in Parametric Nonlinear Programming

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Abstract

We study questions of existence and calculation of directional derivatives of value functions of nonlinear mathematical programming problems depending on parameters. To this end, we use the directional derivatives of the multivalued mappings, defined by the constraints of the problems; this approach was pioneered by Demyanov. We obtain sufficient conditions for existence and explicit formulas for calculating the directional derivatives of the first and second orders, under weaker hypotheses than those traditionally assumed.

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Acknowledgments

The second and third authors’ work was supported by the Belarussian State Program for Fundamental Research “Mathematical Simulation Methods to Complex Systems”. The authors would like to thank Editor-in-Chief, Prof. Franco Giannessi and the two anonymous referees for the valuable remarks that helped to improve the manuscript.

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Authors and Affiliations

  1. Belarusian State University of Informatics and Radioelectronics, Minsk, Belarus

    Alexey Leschov & Leonid Minchenko

  2. Advanced Development and Research, Minneapolis, MN, USA

    Vadim Bondarevsky

Authors
  1. Vadim Bondarevsky
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  2. Alexey Leschov
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  3. Leonid Minchenko
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Correspondence to Leonid Minchenko.

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Bondarevsky, V., Leschov, A. & Minchenko, L. Value Functions and Their Directional Derivatives in Parametric Nonlinear Programming. J Optim Theory Appl 171, 440–464 (2016). https://doi.org/10.1007/s10957-015-0814-9

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  • DOI: https://doi.org/10.1007/s10957-015-0814-9

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