A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems

In our paper, we introduce a sparse and symmetric matrix completion quasi-Newton model using automatic differentiation, for solving unconstrained optimization problems where the sparse structure of the Hessian is available. The proposed method is a kind of matrix completion quasi-Newton method and h...

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Auteurs principaux:	Huiping Cao, Xiaomin An
Format:	article
Langue:	EN
Publié:	MDPI AG 2021
Sujets:	symmetric quasi-Newton method unconstrained optimization problems matrix completion automatic differentiation superlinear convergence Broyden–Fletcher–Goldfarb–Shanno method Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/fd2e320392a24448bd2496d54df4470e
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id	oai:doaj.org-article:fd2e320392a24448bd2496d54df4470e
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spelling	oai:doaj.org-article:fd2e320392a24448bd2496d54df4470e2021-11-25T19:06:41ZA Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems10.3390/sym131120932073-8994https://doaj.org/article/fd2e320392a24448bd2496d54df4470e2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2093https://doaj.org/toc/2073-8994In our paper, we introduce a sparse and symmetric matrix completion quasi-Newton model using automatic differentiation, for solving unconstrained optimization problems where the sparse structure of the Hessian is available. The proposed method is a kind of matrix completion quasi-Newton method and has some nice properties. Moreover, the presented method keeps the sparsity of the Hessian exactly and satisfies the quasi-Newton equation approximately. Under the usual assumptions, local and superlinear convergence are established. We tested the performance of the method, showing that the new method is effective and superior to matrix completion quasi-Newton updating with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and the limited-memory BFGS method.Huiping CaoXiaomin AnMDPI AGarticlesymmetric quasi-Newton methodunconstrained optimization problemsmatrix completionautomatic differentiationsuperlinear convergenceBroyden–Fletcher–Goldfarb–Shanno methodMathematicsQA1-939ENSymmetry, Vol 13, Iss 2093, p 2093 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	symmetric quasi-Newton method unconstrained optimization problems matrix completion automatic differentiation superlinear convergence Broyden–Fletcher–Goldfarb–Shanno method Mathematics QA1-939
spellingShingle	symmetric quasi-Newton method unconstrained optimization problems matrix completion automatic differentiation superlinear convergence Broyden–Fletcher–Goldfarb–Shanno method Mathematics QA1-939 Huiping Cao Xiaomin An A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems
description	In our paper, we introduce a sparse and symmetric matrix completion quasi-Newton model using automatic differentiation, for solving unconstrained optimization problems where the sparse structure of the Hessian is available. The proposed method is a kind of matrix completion quasi-Newton method and has some nice properties. Moreover, the presented method keeps the sparsity of the Hessian exactly and satisfies the quasi-Newton equation approximately. Under the usual assumptions, local and superlinear convergence are established. We tested the performance of the method, showing that the new method is effective and superior to matrix completion quasi-Newton updating with the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method and the limited-memory BFGS method.
format	article
author	Huiping Cao Xiaomin An
author_facet	Huiping Cao Xiaomin An
author_sort	Huiping Cao
title	A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems
title_short	A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems
title_full	A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems
title_fullStr	A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems
title_full_unstemmed	A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems
title_sort	sparse quasi-newton method based on automatic differentiation for solving unconstrained optimization problems
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/fd2e320392a24448bd2496d54df4470e
work_keys_str_mv	AT huipingcao asparsequasinewtonmethodbasedonautomaticdifferentiationforsolvingunconstrainedoptimizationproblems AT xiaominan asparsequasinewtonmethodbasedonautomaticdifferentiationforsolvingunconstrainedoptimizationproblems AT huipingcao sparsequasinewtonmethodbasedonautomaticdifferentiationforsolvingunconstrainedoptimizationproblems AT xiaominan sparsequasinewtonmethodbasedonautomaticdifferentiationforsolvingunconstrainedoptimizationproblems
_version_	1718410318139359232

A Sparse Quasi-Newton Method Based on Automatic Differentiation for Solving Unconstrained Optimization Problems

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