{"ID":2826337,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.19532","arxiv_id":"2512.19532","title":"A perturbed preconditioned gradient descent method for the unconstrained minimization of composite objectives","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.","short_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 dimen...","url_abs":"https://arxiv.org/abs/2512.19532","url_pdf":"https://arxiv.org/pdf/2512.19532v1","authors":"[\"Jea-Hyun Park\",\"Abner J. Salgado\",\"Steven M. Wise\"]","published":"2025-12-22T16:20:26Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"math.NA\"]","methods":"[]","has_code":false}