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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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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