Dr. Fátima Pereira

University of Évora, Portugal



Title of the paper: Geometric Conditions for Well-Posedness in Hilbert Spaces and Directional Curvature in Finite Dimensions


Abstract: Given a closed set C in a Hilbert space H, and a closed, convex, bounded set F ⊂ H, with the origin in its interior, I present some (local) geometric conditions that guarantee the existence and uniqueness of the projection onto C, in the sense of the Minkowski functional of F. To this end, I introduce a (new) formula for computing the curvature of F at points on its boundary. Furthermore, I show that, when H = R n and the boundary of F is given by an implicit equation, this formula is equivalent to an existing one, but is easier to apply.

Bio: To be announced soon




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