Γ-convergence of non-local, non-convex functionals in one dimension

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...

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

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...

Γ-convergence of Graph Ginzburg–landau Functionals

We study Γ-convergence of graph-based Ginzburg–Landau functionals, both the limit for zero diffusive interface parameter ε → 0 and the limit for infinite nodes in the graph m→∞. For general graphs we prove that in the limit ε → 0 the graph cut objective function is recovered. We show that the continuum limit of this objective function on 4-regular graphs is related to the total variation semino...