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arXiv · 2205.10945

A preconditioned deepest descent algorithm for a class of optimization problems involving the $p(x)$-Laplacian operator

Sergio González-Andrade·María de los Ángeles Silva
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Abstract

In this paper we are concerned with a class of optimization problems involving the $p(x)$-Laplacian operator, which arise in imaging and signal analysis. We study the well-posedness of this kind of problems in an amalgam space considering that the variable exponent $p(x)$ is a log-H\"older continuous function. Further, we propose a preconditioned descent algorithm for the numerical solution of the problem, considering a "frozen exponent" approach in a finite dimension space. Finally, we carry on several numerical experiments to show the advantages of our method. Specifically, we study two detailed example whose motivation lies in a possible extension of the proposed technique to image processing.

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Sergio González-Andrade, María de los Ángeles Silva. 2022-05-22. A preconditioned deepest descent algorithm for a class of optimization problems involving the $p(x)$-Laplacian operator. https://arxiv.org/abs/2205.10945

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