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Title: Regularity of a kind of marginal functions in Hilbert spaces
Authors: Goncharov, Vladimir V.
Pereira, Fatima F.
Editors: Butenko, Sergiy
Rassias, Themistocles M.
Floudas, Christodoulos A.
Keywords: marginal function
metric projection
optimal time control problem
Hamilton-Jacobi equation
viscosity solution
uniform rotundity
duality mapping
proximal normals
Fréchet differentiability
Hölder continuity
Issue Date: 2014
Publisher: Springer
Citation: Pereira F., Goncharov V. Regularity of a kind of marginal functions in Hilbert spaces, In: S. Butenko, Ch. Floudas, Th. Rassias (eds). On global optimization in science and engineering, in honor of Prof. Panos Pardalos, 423-464 (2014)
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, 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.
ISBN: 978-1-4939-0807-3
Type: bookPart
Appears in Collections:CIMA - Publicações - Capítulos de Livros

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