Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates

Evolution by Non-Convex Functionals

We establish a semi-group solution concept for morphological differential equations, such as the mean curvature flow equation. The proposed method consists in generating flows from generalized minimizers of nonconvex energy functionals. We use relaxation and convexification to define generalized minimizers. The main part of this work consists in verification of the solution concept by comparing...

Approximation of Non-convex Functionals in Gbv Approximation of Non-convex Functionals in Gbv

A Rigidity Criterion for Non-Convex Polyhedra

Let P be a (non necessarily convex) embedded polyhedron in R, with its vertices on an ellipsoid. Suppose that the interior of P can be decomposed into convex polytopes without adding any vertex. Then P is infinitesimally rigid. More generally, let P be a polyhedron bounding a domain which is the union of polytopes C1, · · · , Cn with disjoint interiors, whose vertices are the vertices of P . Su...

Simultaneous Con dence Intervals for Linear Estimates of Linear Functionals

This note presents three ways of constructing simultaneous condence intervals for linear estimates of linear functionals in inverse problems, including \Backus-Gilbert" estimates. Simultaneous con dence intervals are needed to compare estimates, for example, to nd spatial variations in a distributed parameter. The notion of simultaneous con dence intervals is introduced using coin tossing as an...

Minimization of Non-smooth, Non-convex Functionals by Iterative Thresholding

Numerical algorithms for a special class of non-smooth and non-convex minimization problems in infinite dimensional Hilbert spaces are considered. The functionals under consideration are the sum of a smooth and non-smooth functional, both possibly non-convex. We propose a generalization of the gradient projection method and analyze its convergence properties. For separable constraints in the se...