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Regularity of a Kind of Marginal Functions in Hilbert Spaces

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Abstract

We study well posedness of some mathematical programming problem depending on a parameter that generalizes in a certain sense the metric projection onto a closed nonconvex set. We are interested in regularity of the set of minimizers as well as of the value function, which can be seen, on one hand, as the viscosity solution to a Hamilton–Jacobi equation, while, on the other hand, as the minimal time in some related optimal time control problem. The regularity includes both the Fréchet differentiability of the value function and the Hölder continuity of its (Fréchet) gradient.

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Acknowledgements

Work is fulfilled in framework of the project “Variational Analysis: Theory and Applications” (PTDC/MAT/111809/2009) financially supported by Fundação para Ciência e Tecnologia (FCT), the Portuguese institutions COMPETE, QREN and the European Regional Development Fund (FEDER).

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Authors and Affiliations

  1. CIMA-UE, Rua Romão Ramalho 59, 7000-671, Évora, Portugal

    Fátima F. Pereira & Vladimir V. Goncharov

  2. Institute of Systems Dynamics and Control Theory of Siberian Branch of RAS, ul. Lermontov 134, 664033, Irkutsk, Russia

    Vladimir V. Goncharov

Authors
  1. Fátima F. Pereira
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  2. Vladimir V. Goncharov
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Correspondence to Vladimir V. Goncharov .

Editor information

Editors and Affiliations

  1. Department of Mathematics, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

  2. Princeton University Dept. Chemical Engineering, Princeton, New Jersey, USA

    Christodoulos A. Floudas

  3. Dept. Industrial & Systems Engineering, Texas A&M University, College Station, Texas, USA

    Sergiy Butenko

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Pereira, F.F., Goncharov, V.V. (2014). Regularity of a Kind of Marginal Functions in Hilbert Spaces. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_22

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