Scaling strategies for symmetric rank-one method in solving unconstrained optimization problems

• Main Authors: Mustafa, Mamat, Aliyu Usman, Moyi, Wah June, Leong
• Format: Article
• Language: English
• Published: 2014
• Subjects: QA Mathematics
• Online Access: http://eprints.unisza.edu.my/5079/1/FH02-FIK-14-00733.jpg; http://eprints.unisza.edu.my/5079/
• Institution: Universiti Sultan Zainal Abidin

Symmetric rank-one update (SR1) is known to have good numerical performance among the quasi-Newton methods for solving unconstrained optimization problems as evident from the recent study of Farzin et al. (2011), However, it is well known that the SR1 update may not preserve positive definiteness even when updated from a positive definite approximation and can be undefined with zero denominator. In this paper, we propose some scaling strategies to overcome these well known shortcomings of the SR1 update. Numerical experiment showed that the proposed strategies are very competitive, encouraging and have exhibited a clear improvement in the numerical performance over SR1 algorithms with some existing strategies in avoiding zero denominator and preserving positive-definiteness.