Regularity of a Kind of Marginal Functions in Hilbert Spaces

Fátima F. Pereira () and Vladimir V. Goncharov ()
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Fátima F. Pereira: CIMA-UE
Vladimir V. Goncharov: CIMA-UE

A chapter in Optimization in Science and Engineering, 2014, pp 423-464 from Springer

Abstract: 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.

Keywords: Marginal Function; Time Optimal Control Problem; Hamilton-Jacobi Equation; Solution Viscosity; Uniformly Rotund (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4939-0808-0_22

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DOI: 10.1007/978-1-4939-0808-0_22

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