New Family of Dai–Liao Conjugate Gradient Directions for Large-Scale Unconstrained Optimization with Applications to Image Restoration

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.