Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Statistics Optimization & Information Computing

DOI: 10.19139/soic-2310-5070-3584

Authors: Basim A. Hassan, Talal M. Alharbi, Sulaiman M. Ibrahim, Hashibah Hamid, Salah Mahmoud Boulaaras

Institutions: University of Mosul, Qassim University, A'Sharqiyah University, Sohar University, Universiti Utara Malaysia

Language: English

Topic: Advanced Optimization Algorithms Research

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Qassim University

Award: G92618698