A New Sparse Quasi-Newton Update Method
| Autor: | Rui Diao, Yu-Hong Dai, Minghou Cheng |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Hessian matrix
Hessian automatic differentiation Mathematical optimization Large-scale Matrix completion Quasi-Newton methods Secant condition Sparsity Unconstrained optimization Matrix completion Davidon–Fletcher–Powell formula MathematicsofComputing_NUMERICALANALYSIS Symmetric rank-one symbols.namesake Secant method Broyden–Fletcher–Goldfarb–Shanno algorithm symbols Applied mathematics Quasi-Newton method lcsh:Science (General) lcsh:Q1-390 Mathematics |
| Zdroj: | Sultan Qaboos University Journal for Science, Vol 17, Iss 1, Pp 30-43 (2012) |
| ISSN: | 2414-536X 1027-524X |
| DOI: | 10.24200/squjs.vol17iss1pp30-43 |
| Popis: | Based on the idea of maximum determinant positive definite matrix completion, Yamashita proposed a sparse quasi-Newton update, called MCQN, for unconstrained optimization problems with sparse Hessian structures. Such an MCQN update keeps the sparsity structure of the Hessian while relaxing the secant condition. In this paper, we propose an alternative to the MCQN update, in which the quasi-Newton matrix satisfies the secant condition, but does not have the same sparsity structure as the Hessian in general. Our numerical results demonstrate the usefulness of the new MCQN update with the BFGS formula for a collection of test problems. A local and superlinear convergence analysis is also provided for the new MCQN update with the DFP formula. |
| Databáze: | OpenAIRE |
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