An improved quasi-Newton equation on the quasi-Newton methods for unconstrained optimizations

Basim Abbas Hassan (University of Mosul)
Kanikar Muangchoo (Rajamangala University of Technology Phra Nakhon (RMUTP))
Fadhil Alfarag (University of Birmingham)
Abdulkarim Hassan Ibrahim (King Mongkut’s University of Technology Thonburi (KMUTT))
Auwal Bala Abubakar (1. Bayero University 2. Sefako Makgatho Health Sciences University)

Indonesian Journal of Electrical Engineering and Computer Science
Vol 22, No 2: May 2021

Quasi-Newton methods are a class of numerical methods for solving the problem of unconstrained optimization. To improve the overall efficiency of resulting algorithms, we use the quasi-Newton methods which is interesting for quasi-Newton equation. In this manuscript, we present a modified BFGS update formula based on the new quasi-Newton equation, which give a new search direction for solving unconstrained optimizations proplems. We analyse the convergence rate of quasi-Newton method under some mild condition. Numerical experiments are conducted to demonstrate the efficiency of new methods using some test problems. The results indicates that the proposed method is competitive compared to the BFGS methods as it yielded fewer iteration and fewer function evaluations.