Indonesian Journal of Electrical Engineering and Computer Science Vol. 28, No. 1, October 2022, pp. 551~558 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v28.i1.pp551-558  551 Journal homepage: http://ijeecs.iaescore.com A new three-term conjugate gradient method for training neural networks with global convergence Alaa Luqman Ibrahim 1 , Mohammed Guhdar Mohammed 2 1 Department of Mathematics, Faculty of Science, University of Zakho, Zakho, Iraq 2 Department of Computer Science, Faculty of Science, University of Zakho, Zakho, Iraq Article Info ABSTRACT Article history: Received Mar 28, 2022 Revised Jul 28, 2022 Accepted Aug 4, 2022 Conjugate gradient methods (CG) constitute excellent neural network training methods that are simplicity, flexibility, numerical efficiency, and low memory requirements. In this paper, we introduce a new three-term conjugate gradient method, for solving optimization problems and it has been tested on artificial neural networks (ANN) for training a feed-forward neural network. The new method satisfied the descent condition and sufficient descent condition. Global convergence of the new (NTTCG) method has been tested. The results of numerical experiences on some well- known test function shown that our new modified method is very effective, by relying on the number of functions evaluation and number of iterations, also included the numerical results for training feed-forward neural networks with other well-known method in this field. Keywords: Artificial neural networks Descent condition Global convergent property Sufficient descent condition Three-term conjugate gradient Unconstrained optimization This is an open access article under the CC BY-SA license. Corresponding Author: Moahmmed Guhdar Mohammed Department of Computer Science, Faculty of Science, University of Zakho Zakho, Kurdistan Region, Iraq Email: mohammed.guhdar@uoz.edu.krd 1. INTRODUCTION Artificial neural networks (ANNs) have been used for decades with major success in many applications related to machine learning [1]-[3] due to their outstanding ability to self-adapting and self- learning. They have been used in areas such as robotics, security, and self-driving cars very intensely. They are often more robust and accurate than other classification techniques due to their resilience in problem solving and parallel processing support [4], [5]. Although several different methods for training have been suggested one of which is feed forward neural networks (FNNs), this training pattern is one of the most known and widely used in many various areas and applications. Multi-layer (FNNs) are parallel computational models composed of densely interconnected, adaptive processing units, characterized by an inherent propensity for learning from experience and discovering new knowledge. Due to its excellent self- adaptation and self-learning ability, it gained early popularity in machine learning [1], [2], [6] and are often found it to be more efficient. The process of a FNN is depend on the below formula:    =∑   −1,   −1 +   ,  −1 =1    = (   ) (1) where the sum of its weighted inputs is    , for the  ℎ node in the  ℎ layer ( = 1, . . . , ),   −1, are the weights from the  ℎ neuron at the ) layer to the  ℎ neuron at the  ℎ layer,    is the bias of the  ℎ neuron at the  ℎ layer,    is the outputof the  ℎ neuron that belongs to the  ℎ layer, and (   ), is the  ℎ neuron activation function.