Variational analysis for a class of minimal time functions in Hilbert spaces

Document Type

Article

Publication Date

1-1-2004

Abstract

This paper considers the parameterized infinite dimensional optimization problem minimize {t ≥ 0 : S ∩ {x + tF} ≠ ø}, where S is a nonempty closed subset of a Hilbert space H and F ⊆ H is closed convex satisfying 0 ∈ int F. The optimal value T(x) depends on the parameter x ∈ H, and the (possibly empty) set S∩(x+T(x)F) of optimal solutions is the "F-projection" of x into S. We first compute proximal and Fréchet subgradients of T(·) in terms of normal vectors to level sets, and secondly, in terms of the F-projection. Sufficient conditions are also obtained for the differentiability and semiconvexity of T(·), results which extend the known case when F is the unit ball.

Publication Source (Journal or Book title)

Journal of Convex Analysis

First Page

335

Last Page

361

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