Another hybrid conjugate gradient method as a convex combination of NVHS$^*$ and CD methods
Volume 53 / 2026
Applicationes Mathematicae 53 (2026), 193-204
MSC: Primary 90C30; Secondary 65K05, 62G05
DOI: 10.4064/am2559-2-2026
Published online: 26 September 2026
Abstract
Conjugate gradient methods play a fundamental role in solving unconstrained optimization problems. We propose a new hybrid conjugate gradient algorithm that forms a convex combination of $\beta _{k}^{{\rm NVHS}^{\ast }}$ and $\beta _{k}^{\rm CD}$. The parameter $\theta _{k} $ is determined so as to satisfy the conjugacy condition. Under the strong Wolfe line search conditions, we establish both the descent property and the global convergence of the proposed hybrid method. Numerical experiments demonstrate that the new method is robust and computationally efficient.
