A Variant of Self-Adjusting Spectral Hybrid Dai-Liao Conjugate Gradient Method

Abstract

The Conjugate Gradient method is a popular optimization technique known for its fast convergence and low memory requirements. These advantages make it efficient for solving unconstrained problems of various scales. This study presents a spectral convex combination modification of the Liu Storey method for unconstrained optimization. The method approximates the step size while preserving descent properties, aiming to enhance efficiency and adaptability compared to existing approaches.
The proposed method generates search directions that inherently satisfy the sufficient descent property, regardless of the conjugate parameter or line search choice. The study concludes by validating the impact and adaptability of various parameter combinations on the effectiveness of the spectral hybrid method for solving unconstrained optimization problems. Numerical experiments demonstrate the efficiency of the proposed methods in terms of iteration count and CPU time, comparing favorably
with current approaches for addressing unconstrained optimization problems.