Quasi-convex combination of three conjugate gradient directions

This research work introduces a novel hybrid conjugate gradient algorithm that combines three descent directions, namely [Formula: see text], [Formula: see text], and [Formula: see text], in a quasi-convex manner. The algorithm aims to construct a direction that closely approximates the Newton direction using the secant equation. To ensure convergence, appropriate hybridization parameters are determined, which not only approximate the Newton direction but also remain bounded. The descent property of the algorithm has been proven, and its global convergence has been demonstrated. Experimental results confirm the efficiency of our new algorithm, surpassing the (DY), (HS), (DL) algorithms in many cases.