We describe two modified secant equations proposed by Yuan, Li and Fukushima. First, we study the approach proposed by Andrei. Then, we explain two hybrid conjugate gradient methods for unconstrained optimization problems. The methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. It is shown that one of the algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. Two approaches for computing the initial value of the steplength proposed by Babaie, Fatemi, and Mahdavi-Amiri and Andrei are used for accelerating the performance of the line search. We implement the algorithms and compare the...
We describe two modified secant equations proposed by Yuan, Li and Fukushima. First, we study the approach proposed by Andrei. Then, we explain two hybrid conjugate gradient methods for unconstrained optimization problems. The methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugate gradient methods. It is shown that one of the algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. Two approaches for computing the initial value of the steplength proposed by Babaie, Fatemi, and Mahdavi-Amiri and Andrei are used for accelerating the performance of the line search. We implement the algorithms and compare the...