THREE-TERM HYBRID BFGS-CG METHOD FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS
O. O. OKUNDALAYE *
Department of Mathematical Sciences, Faculty of Science Adekunle Ajasin University, AkungbaAkoko (AAUA) P.M.Box 01, Akungba Akoko, Ondo State, Nigeria.
*Author to whom correspondence should be addressed.
In solving unconstrained optimization problems, both quasi-Newton and conjugate gradient methods are known to be efficient methods. Hence, three-term Broyden-Flethcher-Goldfarb-Shanno-Conjugate Gradient method is proposed, which combines the strength of both BFGS and CG methods. The method is based on an existing hybrid BFGS-CG method. The Three-term BFGS-CG method, when utilized in solving some selected unconstrained optimization problems, resulted in improvement in the total number of iterations and CPU time. I also prove that the hybrid method is globally convergent.
Keywords: BFGS method, search direction, step-length, global convergence, performance profile