New Conjugate Direction Method for Unconstrained Optimization

The aim of this article is to introduce a new conjugate direction method (CDM) which satisfies a conjugate and descent property to solve an unconstrained optimization problem. The objective function is differentiable and the gradient (first derivative of the objective function) is Lipchitz continuous. The new direction is computed based on the last direction with a new parameter as a coefficient of the next gradient of the given objective function. We consider Numerical examples, with the help of the MATLAB program, using the new method compared with the Fletcher-Reeves conjugate gradient (F-R-CGM) method to verify the effectiveness of the new CDM.Our results are reported as a table containing total iterations and function evaluation.