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Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

Imre Csiszár, František Matúš (2012)

Kybernetika

Integral functionals based on convex normal integrands are minimized subject to finitely many moment constraints. The integrands are finite on the positive and infinite on the negative numbers, strictly convex but not necessarily differentiable. The minimization is viewed as a primal problem and studied together with a dual one in the framework of convex duality. The effective domain of the value function is described by a conic core, a modification of the earlier concept of convex core. Minimizers...

Global calibrations for the non-homogeneous Mumford-Shah functional

Massimiliano Morini (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Using a calibration method we prove that, if Γ Ω is a closed regular hypersurface and if the function g is discontinuous along Γ and regular outside, then the function u β which solves Δ u β = β ( u β - g ) in Ω Γ ν u β = 0 on Ω Γ is in turn discontinuous along Γ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional Ω S u | u | 2 d x + n - 1 ( S u ) + β Ω S u ( u - g ) 2 d x , over S B V ( Ω ) , for β large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.

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