Indonesian Journal of Electrical Engineering and Computer Science Vol. 21, No. 1, January 2021, pp. 505~515 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v21.i1. pp505-515  505 Journal homepage: http://ijeecs.iaescore.com Show off the efficiency of dai-liao method in merging technology for monotonous non-linear problems Rana Z. Al-Kawaz, Abbas Y. Al-Bayati Department of Mathematics, College of Basic Education, University of Telafer, Mosul, Iraq Article Info ABSTRACT Article history: Received May 16, 2020 Revised Jul 20, 2020 Accepted Aug 4, 2020 In this article, we give a new modification for the Dai-Liao method to solve monotonous nonlinear problems. In our modification, we relied on two important procedures, one of them was the projection method and the second was the method of damping the quasi-Newton condition. The new approach of derivation yields two new parameters for the conjugated gradient direction which, through some conditions, we have demonstrated the sufficient descent property for them. Under some necessary conditions, the new approach achieved global convergence property. Numerical results show how efficient the new approach is when compared with basic similar classic methods. Keywords: Dai-Liao method Damping technology Global convergence Projection method Quasi-Newton condition This is an open access article under the CC BY-SA license. Corresponding Author: Rana Z. Al-Kawaz Department of Mathematics University of Telafer College of Basic Education, Mosul, Iraq Email: rana.alkawaz@yahoo.com 1. INTRODUCTION The issue in this article is the assumption of finding the vector value x  , i.e. as in:    ()   (1) When        is continuous and monotonous and satisfy (()  ())  ()  . Methods for solving this type of problem vary when they are not restricted to Newton's method and quasi-Newton methods, and they are preferred due to the convergence of their local lines to the second and local levels. When dealing with large- scale nonlinear equations, the so-called Conjugate Gradient (CG) method of all kinds is effective [1-8]. Applications and innovations continue around these technologies to this day [9-11]. The monotonic equations arose in several different practical situations for example see [12]. The most important advantage of CG-methods is that the direction of the search does not require the calculation of the Jacobin matrix which leads to low math requirements on each iteration. Likewise, when these methods overlap with the projection technique proposed by Solodov and Svaiter [13] to solve large-scale nonlinear equations and constrained nonlinear equations that some researchers have expanded as in [14-19]. Recently, many researchers have presented articles on how to find the solution to both constrained and unconstrained monotones (1) and give them a lot of attention [20-27]. Include the idea of projection that needs to be accelerated using a monotonous case F by monotony F and letting         , the hyperplane: H *    |(  )  (    )  + .