Abstract
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.
Keywords
Publication details
- DOI
- 10.24200/squjs.vol17iss1pp30-43
- Journal
- Sultan Qaboos University Journal for Science, 16, 30
- Publisher
- Sultan Qaboos University
- Open access
- Gold open access
- License
- CC BY 4.0
Cite this article
APA 7
Cheng, M., Dai, Y., & Diao, R. (2012). A New Sparse Quasi-Newton Update Method. Sultan Qaboos University Journal for Science, 16, 30. https://doi.org/10.24200/squjs.vol17iss1pp30-43
MLA 9
Cheng, Minghou, et al. "A New Sparse Quasi-Newton Update Method." Sultan Qaboos University Journal for Science, vol. 16, 2012, pp. 30. https://doi.org/10.24200/squjs.vol17iss1pp30-43.
Chicago (author–date)
Cheng, Minghou, Yu‐Hong Dai, and Rui Diao. 2012. "A New Sparse Quasi-Newton Update Method." Sultan Qaboos University Journal for Science 16: 30. https://doi.org/10.24200/squjs.vol17iss1pp30-43.
Harvard
Cheng, M., Dai, Y. and Diao, R. (2012) 'A New Sparse Quasi-Newton Update Method', Sultan Qaboos University Journal for Science, 16, pp. 30. doi:10.24200/squjs.vol17iss1pp30-43.
Vancouver
Cheng M, Dai Y, Diao R. A New Sparse Quasi-Newton Update Method. Sultan Qaboos University Journal for Science. 2012;16:30. doi:10.24200/squjs.vol17iss1pp30-43
IEEE
M. Cheng, Y. Dai, and R. Diao, "A New Sparse Quasi-Newton Update Method," Sultan Qaboos University Journal for Science, vol. 16, pp. 30, 2012, doi: 10.24200/squjs.vol17iss1pp30-43.