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Journal of Control Science and Engineering
Volume 2015, Article ID 674617, 8 pages
Research Article

A New BFGS Algorithm Using the Decomposition Matrix of the Correction Matrix to Obtain the Search Directions

Teaching Department, Jilin City Radio and TV University, Jilin 132002, China

Received 30 September 2014; Revised 3 January 2015; Accepted 3 January 2015

Academic Editor: Shengwei Mei

Copyright © 2015 Li Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an improved method for determining the search direction in the BFGS algorithm. Our approach uses the equal inner product decomposition method for positive-definite matrices. The decomposition of an approximated Hessian matrix expresses a correction formula that is independent from the exact line search. This decomposed matrix is used to compute the search direction in a new BFGS algorithm.