A Novel Hybrid Conjugate Gradient Algorithm for Solving Unconstrained Optimization Problems

Abstract

We introduce a novel hybrid conjugate gradient method for unconstrained optimization, combining the AlBayati-AlAssady and Wei-Yao-Liu approaches, where the convex parameter is determined using the conjugacy condition. Through rigorous theoretical analysis, we establish that the proposed method guarantees sufficient descent properties and achieves global convergence under the strong Wolfe conditions. Using the performance profile of Dolan and Moré, we confirm that our method, denoted as RN, consistently outperforms both classical (HS, FR, PRP and DY CG) and hybrid (BAFR and BADY) methods, particularly for large-scale problems.