This paper addresses the critical challenge of designing efficient and robust conjugate gradient (CG) methods for large-scale unconstrained optimization, where classical CG variants often suffer from insufficient descent properties and convergence failures without restrictive line searches. We introduce two novel Dai-Liao-type CG variants, BH and BI, derived via functional approximations that incorporate objective reduction and curvature information within the Dai-Liao conjugacy framework. Important features of the proposed methods include the inherently satisfying of sufficient descent condition independent of the line search and preserving conjugacy while enhancing adaptability through problem-dependent scaling parameters. The global convergence is established under standard assumptions (Lipschitz gradients, convex level sets). Extensive numerical experiments on set of large-scale test problems demonstrate that the proposed algorithms significantly outperform some classical CG methods in iterations, function evaluations and CPU time. Performance profiles confirm their superior efficiency and robustness.
Hassan et al. (Sun,) studied this question.