Evolution by Non-Convex Functionals

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...

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...

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

Non-convex, non-local functionals converging to the total variation

Article history: Received 14 November 2016 Accepted 14 November 2016 Available online 12 December 2016 Presented by Haïm Brézis We present new results concerning the approximation of the total variation, ∫ |∇u|, of a function u by non-local, non-convex functionals of the form δ(u)= ∫ ∫ δφ (|u(x)− u(y)|/δ) |x− y|d+1 dxdy, as δ → 0, where is a domain in Rd and φ : [0, +∞) → [0, +∞) is a non-decre...

Generalized convex functionals

This paper studies functionals defined by multiple integrals associated to differential forms on the jet bundle of first order corresponding to some Riemannian manifolds; the domain of these functionals consists in submanifold maps satisfying certain conditions of integrability. Our idea is to give geometric properties to the domain of a functional allowing us to properly define convexity. The ...