A Sufficient Descent Dai-Liao Type Conjugate Gradient Update Parameter

Abstract

In recent years, conjugate gradient methods have gained popularity as efficient iterative techniques for unconstrained optimization problems without the need for matrix storage. Based on the Dai-Laio conjugacy condition, this article presents a new hybrid conjugate gradient method that combines features of the Dai-Yuan and Dai-Laio methods. The proposed method addresses the numerical instability and slow convergence of the Dai-Yuan method as well as the potential poor performance of the Dai-Laio method in highly non-linear optimization problems. The hybrid method solves optimization problems with faster convergence rates and greater stability by combining the advantages of both methods. The resulting algorithm is shown to be more effective and reliable, and theoretical analysis reveals that it has sufficient descent properties. The proposed method's competitive performance is shown through a number of benchmark tests and comparisons with other approaches, indicating that it has the potential to be an effective approach for complex, unconstrained optimization.