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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.19532 |
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| _version_ | 1866912783093727232 |
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| author | Park, Jea-Hyun Salgado, Abner J. Wise, Steven M. |
| author_facet | Park, Jea-Hyun Salgado, Abner J. Wise, Steven M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19532 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A perturbed preconditioned gradient descent method for the unconstrained minimization of composite objectives Park, Jea-Hyun Salgado, Abner J. Wise, Steven M. Optimization and Control Numerical Analysis 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. |
| title | A perturbed preconditioned gradient descent method for the unconstrained minimization of composite objectives |
| topic | Optimization and Control Numerical Analysis |
| url | https://arxiv.org/abs/2512.19532 |