Bregman Distances in Inverse Problems and Partial Differential Equations

Martin Burger ()
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Martin Burger: Westfälische Wilhelms-Universität (WWU) Münster. Einsteinstr. 62

A chapter in Advances in Mathematical Modeling, Optimization and Optimal Control, 2016, pp 3-33 from Springer

Abstract: Abstract The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman distances, which have evolved to a standard tool in these fields in the last decade. Moreover, we discuss related issues in the analysis and numerical analysis of nonlinear partial differential equations with a variational structure. For such problems Bregman distances appear to be of similar importance, but are currently used only in a quite hidden fashion. We try to work out explicitly the aspects related to Bregman distances, which also lead to novel mathematical questions and may also stimulate further research in these areas.

Keywords: Planck Equation; Nonlinear Evolution Equation; Optimal Transport; Lyapunov Functional; Convex Functional (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-30785-5_2

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DOI: 10.1007/978-3-319-30785-5_2

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