The Optimization Problem for Functions of Bounded Variation

Abstract

For a function of bounded variation f in

{\mathbb{R}}^n

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mathbb {R}^n$$\end{document}

, we consider the optimization problem of affine total variation, subject to a constraint on the LYZ body

⟨f⟩

\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\langle f\rangle $$\end{document}

under affine transformations, along with its dual problem. As applications, we also derive properties of the solutions to the related optimization problem, as well as properties of the LYZ body.

Keywords

Function of bounded variation / John ellipsoid / Jensen’s inequality

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Funding

National Natural Science Foundation of China(12371060)

RIGHTS & PERMISSIONS

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature