A perturbed preconditioned gradient descent method for the unconstrained minimization of composite objectives

Jea-Hyun Park; Abner J. Salgado; Steven M. Wise

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arXiv · 2512.19532

A perturbed preconditioned gradient descent method for the unconstrained minimization of composite objectives

Jea-Hyun Park·Abner J. Salgado·Steven M. Wise

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Abstract

We introduce a perturbed preconditioned gradient descent (PPGD) method for the unconstrained minimization of a strongly convex objective $G$ with a locally Lipschitz continuous gradient. We assume that $G(v)=E(v)+F(v)$ and that the gradient of $F$ is only known approximately. Our analysis is conducted in infinite dimensions with a preconditioner built into the framework. We prove a linear rate of convergence, up to an error term dependent on the gradient approximation. We apply the PPGD to the stationary Cahn-Hilliard equations with variable mobility under periodic boundary conditions. Numerical experiments are presented to validate the theoretical convergence rates and explore how the mobility affects the computation.

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BibTeX RIS

Jea-Hyun Park, Abner J. Salgado, Steven M. Wise. 2025-12-22. A perturbed preconditioned gradient descent method for the unconstrained minimization of composite objectives. https://arxiv.org/abs/2512.19532

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