Radiality and semismoothness

Semismooth Newton Methods for Operator Equations in Function Spaces

We develop a semismoothness concept for nonsmooth superposition operators in function spaces. The considered class of operators includes NCP-function-based reformulations of infinite-dimensional nonlinear complementarity problems, and thus covers a very comprehensive class of applications. Our results generalize semismoothness and -order semismoothness from finite-dimensional spaces to a Banach...

Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization

We show that a locally Lipschitz homeomorphism function is semismooth at a given point if and only if its inverse function is semismooth at its image point. We present a sufficient condition for the semismoothness of solutions to generalized equations over cone reducible (nonpolyhedral) convex sets. We prove that the semismoothness of solutions to the Moreau-Yosida regularization of a lower sem...

Differentiability and semismoothness properties of integral functions and their applications

In this paper we study differentiability and semismoothness properties of functions defined as integrals of parameterized functions. We also discuss applications of the developed theory to the problems of shape-preserving interpolation, option pricing and semi-infinite programming.

Investigating the maturation of microstructure and radial orientation in the preterm human cortex with diffusion MRI

Preterm birth disrupts and alters the complex developmental processes in the cerebral cortex. This disruption may be a contributing factor to widespread delay and cognitive difficulties in the preterm population. Diffusion-weighted magnetic resonance imaging (DW MRI) is a noninvasive imaging technique that makes inferences about cellular structures, at scales smaller than the imaging resolution...

Radiality: A Tongan Cultural Model