Following the setting of the Dai-Liao (DL) parameter in conjugate gradient (CG) methods‎, ‎we introduce two new parameters based on the modified secant equation proposed by Li et al‎. ‎(Comput‎. ‎Optim‎. ‎Appl‎. ‎202:523-539‎, ‎2007) with two approaches‎, ‎which use an extended new conjugacy condition‎. ‎The first is based on a modified descent three-term search direction‎, ‎as the descent Hest...

In this paper, a new family of Dai-Liao–type conjugate gradient methods are proposed for unconstrained optimization problem. the methods, modified secant equation used in [H. Yabe and M. Takano, Comput. Optim. Appl. 28 (2004) 203–225] is considered Dai Liao’s conjugacy condition. Under some certain assumptions, we show that our globally convergent general functions with strong Wolfe line search...

Following the approach proposed by Dai and Liao, we introduce two nonlinear conjugate gradient methods for unconstrained optimization problems. One of our proposedmethods is based on a modified version of the secant equation proposed by Zhang, Deng and Chen, and Zhang and Xu, and the other is based on the modified BFGS update proposed by Yuan. An interesting feature of our methods is their acco...

In this paper, by linearly combining the numerator and denominator terms of Dai-Liao (DL) Bamigbola-Ali-Nwaeze (BAN) conjugate gradient methods (CGMs), a general form DL-BAN method has been proposed. From form, new hybrid CGM, which was found to possess sufficient descent property is generated. Numerical experiment carried out on CGM in comparison with four existing CGMs, using some set large s...

In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai–Liao condition and descent three-term CG search direction. Both are incorporated with projection technique for solving large-scale monotone nonlinear equations. Using Lipschitz assumptions, global convergence of methods has been proved. Finally, numerical results provided to illustrate robustness methods.

We propose an effective conjugate gradient method belonging to the class of Dai–Liao methods for solving unconstrained optimization problems. employ a variant modified secant condition and introduce new parameter by problem. The problem combines well-known features linear using some penalty functions. This takes advantage function information as well provide iterations. Our proposed is globally...

The conjugate gradient method is one of the most popular methods to solve large-scale unconstrained optimization problems since it does not require second derivative, such as Newton’s or approximations. Moreover, can be applied in many fields neural networks, image restoration, etc. Many complicated are proposed these functions two three terms. In this paper, we propose a simple, easy, efficien...