Optimization refers to the process of finding the best possible solution to a problem within a given set of constraints. It involves maximizing or minimizing a specific objective function while adhering to specific constraints. Optimization is used in various fields, including mathematics, engineering, economics, computer science, and data science, among others. The objective function can be a simple equation, a complex algorithm, or a mathematical model that describes a system or process. There are various optimization techniques available, including linear programming, nonlinear programming, genetic algorithms, simulated annealing, and particle swarm optimization, among others. These techniques use different algorithms to search for the optimal solution to a problem. In this paper, the main goal of unconstrained optimization is to minimize an objective function that uses real variables and has no value restrictions. In this study, based on the modified conjugacy condition, we offer a new conjugate gradient (CG) approach for nonlinear unconstrained problems in optimization. The new method satisfied the descent condition and the sufficient descent condition. We compare the numerical results of the new method with the Hestenes-Stiefel (HS) method. Our novel method is quite effective according to the number of iterations (NOI) and the number of functions (NOF) evaluated, as demonstrated by the numerical results on certain well-known non-linear test functions.

In this paper, we suggest a new coefficient conjugate gradient method for nonlinear unconstrained optimization by using two parameters one of them is parameter of (FR) and the other one is parameter of (CD), we give a descent condition of the suggested method.

In this paper , we suggested a new conjugate gradient algorithm for unconstrained optimization based on logistic mapping, descent condition and sufficient descent condition for our method are provided. Numerical results show that our presented algorithm is more efficient for solving nonlinear unconstrained optimization problems comparing with (DY) .