Sergio González-Andrade, María de los Ángeles Silva, A preconditioned descent algorithm for a class of optimization problems with the p(x)-Laplacian operator
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DOI: 10.23952/jano.8.2026.2.02
Volume 8, Issue 2, 1 August 2026, Pages 181-200
Abstract. In this paper, we are concerned with an optimization problem involving the p(x)-Laplacian operator, which serves as a model for a broader class of variational problems. We begin with a brief introduction to variable exponent spaces and study the well-posedness of the problem in a suitable functional framework, assuming that its exponent is log-Hölder continuous. For the numerical solution, we propose a preconditioned descent algorithm based on a “frozen exponent” strategy in finite-dimensional settings. We apply the method to two representative cases: the Poisson equation and a denoising-type problem. In both situations, numerical experiments are carried out to highlight the strengths of the proposed approach. Our main interest is to investigate the performance and practical potential of this class of preconditioned descent algorithms in solving nonlinear variational problems involving variable exponent operators.
How to Cite this Article:
S. González-Andrade, M.D.L.A. Silva, A preconditioned descent algorithm for a class of optimization problems with the p(x)-Laplacian operator, J. Appl. Numer. Optim. 8 (2026), 181-200.