Neighbourhood Retractions of Nonconvex Sets in a Hilbert Space via Sub linear Functionals

作者：Goncharov Vladimir V^*; Pereira Fatima F

来源：Journal of Convex Analysis, 2011, 18(1): 1-36.

• Time-minimum problem
• Minkowski functional
• generalized projection
• strict convexity
• curvature
• proximal normals

For a closed subset C of a Hilbert space (H, parallel to.parallel to) rip and for a sublinear functional rho : H -> R+, which is equivalent to the norm parallel to.parallel to, we give conditions guaranteeing existence and uniqueness of the nearest points to C in the sense of the semidistance generated by rho. This permits us to construct a continuous retraction onto C well defined in a neighbourhood U superset of C. In particular, according to one of the conditions, U can be represented in terms of balance between the local strict convexity modulus of rho and the measure of nonconvexity of the set C at each point.

• 出版日期2011