Journal article
Cubic regularization in symmetric rank-1 quasi-Newton methods
Mathematical programming computation, v 10(4), pp 457-486
01 Dec 2018
Abstract
Quasi-Newton methods based on the symmetric rank-one (SR1) update have been known to be fast and provide better approximations of the true Hessian than popular rank-two approaches, but these properties are guaranteed under certain conditions which frequently do not hold. Additionally, SR1 is plagued by the lack of guarantee of positive definiteness for the Hessian estimate. In this paper, we propose cubic regularization as a remedy to relax the conditions on the proofs of convergence for both speed and accuracy and to provide a positive definite approximation at each step. We show that the n-step convergence property for strictly convex quadratic programs is retained by the proposed approach. Extensive numerical results on unconstrained problems from the CUTEr test set are provided to demonstrate the computational efficiency and robustness of the approach.
Metrics
Details
- Title
- Cubic regularization in symmetric rank-1 quasi-Newton methods
- Creators
- Hande Y. Benson - Drexel UniversityDavid F. Shanno - Rutgers, The State University of New Jersey
- Publication Details
- Mathematical programming computation, v 10(4), pp 457-486
- Publisher
- Springer Nature
- Number of pages
- 30
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Decision Sciences (and Management Information Systems)
- Web of Science ID
- WOS:000448393800001
- Scopus ID
- 2-s2.0-85054680701
- Other Identifier
- 991019169351504721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Computer Science, Software Engineering
- Mathematics, Applied
- Operations Research & Management Science