Multi-steps symmetric rank-one update for unconstrained optimization

• Main Authors: Modarres, Farzin, Abu Hassan, Malik, Leong, Wah June
• Format: Article
• Language: English
• Published: IDOSI Publications 2009
• Online Access: http://psasir.upm.edu.my/id/eprint/15755/1/Multi-steps%20symmetric%20rank-one%20update%20for%20unconstrained%20optimization..pdf; http://psasir.upm.edu.my/id/eprint/15755/; https://www.idosi.org/wasj/wasj7(5)2009.htm

In this paper, we present a generalized Symmetric Rank-one (SR1) method by employing interpolatory polynomials in order to possess a more accurate information from more than one previous step. The basic idea is to incorporate the SR1 update within the framework of multi-step methods. Hence iterates could be interpolated by a curve in such a way that the consecutive points define the curves. However to preserve the positive definiteness of the SR1 updates a restart procedure is applied, in which we restart the SR1 update by a scale of the identity. Comparison to multi-steps BFGS method, the proposed algorithm shows significant improvements in numerical results.