Extra Dai-Liao Method in Conjugate Gradient Method for Solving Minimization Problems

Abstract

This study explores different strategies for setting parameters in optimization algorithms, focusing on refining the Dai–Liao (DL) conjugate gradient method by using a modified quasi-Newton framework. The DL version of the conjugate gradient method is known for its effectiveness in addressing large-scale unconstrained optimization challenges. Nonetheless, conventional implementations often depend on differences between successive iterates and gradient vectors, which can limit adaptability and convergence capabilities in certain circumstances. To overcome these limitations, the proposed method introduces an innovative parameter formula that utilizes the curvature condition differently by incorporating objective function values, instead of just relying on point and gradient differences. This use of function values offers more detailed insights into the optimization landscape, thereby enhancing both the stability and accuracy of the search direction. The main benefit of this modification is its augmented computational efficiency and its capacity to ensure global convergence under relatively mild and realistic conditions. Theoretical analysis, including a proof of global convergence for the new method, supports these assertions. To verify the practical effectiveness of this approach, extensive numerical experiments were carried out on various standard test problems. The results consistently show that the modified method surpasses the traditional DL conjugate gradient algorithm in terms of convergence speed and robustness, confirming the theoretical enhancements and underscoring its potential for wider use in nonlinear optimization.