Sufficient - Descent Scaled Conjugate Gradient Direction for Large-Scale Unconstrained Optimization

Sulaiman Mohammed Ibrahim, Lawal Muhammad, Habibulla Ahadkulov, & Mohd Kamal M. Nawawi
dx.doi.org/10.17576/apjitm-2026-1501-12

Abstract

Conjugate gradient (CG) methods are extensively utilized for solving large-scale unconstrained optimization problems due to their low memory requirements and strong practical performance. However, achieving descency property and maintaining efficiency across diverse optimization landscapes remains challenging. This study addresses these limitations by introducing a novel scaled conjugate gradient direction that integrates a self-scaling parameter into the classical framework. The proposed methodology derives from quasi-Newton principles, ensuring the sufficient descent condition independent of line search precision. Numerical experiments on 120 benchmark problems from the CUTEr library, spanning dimensions from 2 to 600,000 variables, demonstrate the robustness and efficiency of the scaled method.

keyword

Scaled conjugate gradient method, Sufficient descent properties, Benchmark problems.

Area

Data Mining and Optimization