New coefficient of three-term conjugate gradient method for solving unconstrained optimization problems

Recently, Three-Term Conjugate Gradient (TTCG) has become a research trend for solving unconstrained optimization problems. Unfortunately, the problems arise when the existing TTCG methods could only be used by inexact line search. If exact line search is applied, then the formula of TTCG will be reduced to the standard CG method. Therefore, there is a need to come out with a new coefficient of TTCG method that could be used with exact line search. Thus, this paper proposed a new coefficient of TTCG that is suitable to be used by both exact and inexact line search. The proposed formula satisfies both sufficient descent condition and global convergence properties under exact line search. Result analysis performance profile of numerical computation on the different initial point and some optimization problems had shown the robustness and efficiency of this new three term coefficient.