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

Abstract

This paper investigates alternative strategies for constructing parameters within optimization algorithms, with a particular emphasis on enhancing the Dai–Liao (DL) conjugate gradient method through a modified quasi-Newton framework. The conjugate gradient method, especially the DL variant, is widely recognized for its efficiency in solving large-scale unconstrained optimization problems. However, traditional implementations typically rely on differences in iterates and gradient vectors, which may limit their adaptability and convergence properties in certain scenarios. To address these limitations, the proposed approach introduces a novel parameter formula that leverages the curvature condition in a new way-by incorporating information from objective function values, rather than depending solely on differences between points and gradients. This integration of function value data provides richer information about the optimization landscape, which can enhance both the stability and accuracy of the search direction. The primary advantage of this modification lies in its improved computational efficiency and its ability to guarantee global convergence under relatively mild and realistic assumptions. Theoretical analysis is provided to support these claims, including a proof of global convergence for the proposed method. To validate the practical effectiveness of the new approach, comprehensive numerical experiments were conducted on a variety of standard test problems. The results consistently demonstrate that the modified method outperforms the traditional DL conjugate gradient algorithm in terms of convergence speed and robustness, confirming the theoretical improvements and highlighting its potential for broader application in nonlinear optimization.