A Spectral Dai–Liao Conjugate Gradient Method With Strong Theoretical Guarantees for Image Restoration and Machine Learning

ABSTRACT Based on a class of adaptive Dai–Liao parameters (4OR‐Q J Oper Res, 2017, 15: 85–92), this paper proposes a novel Dai–Liao parameter with an explicit upper bound by minimizing the spectral condition number of the search direction matrix, significantly enhancing algorithmic stability. To further strengthen theoretical guarantees, a spectral parameter is designed to ensure the Dai–Liao conjugate gradient method (DL‐CGM) with sufficient descent property under the standard Wolfe conditions. Moreover, the global convergence is established for general functions under mild conditions. Numerical experiments on unconstrained optimization problems, image restoration and machine learning demonstrate the effectiveness and applicability of the proposed method compared to existing CGMs.