An adaptive search direction algorithm for the modified projection minimization optimization

Abstract

In this paper, we proposed a double-search direction algorithm with a free of derivatives based on a different parameter update (n k ) which gives us an update on the double search trend. We used anewly updated formula for the projection parameter within the formula for the proposed search direction. When comparing our numerical results for the proposed algorithm with some standard published algorithmswe obtain efficient numerical results. The proposed algorithm, especially, isused to solve large-scale nonlinear problems by combining two search directions in one search direction. Also, to demonstrate the general convergence of the proposed new algorithm under some circumstances. The numerical performance of the new proposed algorithm on some nonlinear test functions proved the efficiency of this algorithm.