Malaysian Journal of Mathematical Sciences, September 2026, Vol. 20, No. 3
A $\mathbf{DL}$-like Hybrid of $\mathbf{DY}$ Conjugate Gradient Algorithm for Unconstrained Optimization Problems with Application in Mode Function
Ayinde, S. A., Mehamdia, A. E., Adelodun, J. F., and Oyeniyi, K. B.
Corresponding Email: ayindes@babcock.edu.ng
Received date: 16 July 2025
Accepted date: 19 December 2025
Abstract:
Conjugate gradient methods have come a long way in solving system of equations and large scaled optimization problems. In this paper, a hybrid conjugate gradient method which incorporates the DY update parameter and herein constructed conjugate gradient solver that uses Dai-Liao conjugacy conditions is proposed for nonlinear unconstrained optimization problems. It is shown that this proposed method possesses descent search direction at every iteration and thereby converges globally under standard Wolfe line search conditions. Proofs of its robustness and efficiency were demonstrated through numerical tests and application to mode function when compared with other known optimization conjugate gradient algorithms.
Keywords: global convergence; unconstrained optimization; standard Wolfe conditions; descent direction; step length.
