Comparison of three modified Conjugate Gradient methods to solve unconstrained optimization problems / Siti Aminah Abdullah & Nur Anisah Najwa Mohd Arizi

In Mathematical problems, optimization is a technique for finding minimization or maximization in order to find the best value of a function. This project is conducted to solve unconstrained optimization problem using numerical method. One of the numerical method that can be used to solve optimization problems is Conjugate Gradient (CG) method as it is one of the most used method in solving large scale unconstrained optimization problems. There are many types of CG method such as classical, parameterize, scalar, hybrid and modified CG. In this research, it focuses on three modified CG method due the nice descent and convergent properties rather than existing CG method. These modification were proposed by some researchers to increase the efficiency by adding three different third term for each method. The chosen three modified CG methods are the modification of RMIL which has been proposed by Khadijah et al. denoted as SKRMI, the modification of RMIL which has been proposed by Norrdin et al. denoted as Method 2 and the modification of PRP which has been proposed by Zhang et al. denoted as MPRP method. All these methods were tested with five different test functions and different initial points. Then, it will be compared based on its performances by evaluating the number of iteration and CPU times. Thus, the best method among these modified CG will be determined.