A family of Dai-Liao conjugate gradient methods with strong convergence for Image restoration and Machine learning

Abstract Conjugate gradient method is one of the most effective schemes to deal with large-scale optimization problems. In this study, three classes of parameters for the Dai-Liao conjugate condition are provided to be chosen, and thus a new Dai-Liao conjugate parameter is derived. Making a truncation for the conjugate parameter and introducing a restart procedure into the search direction, a family of improved Dai-Liao conjugate gradient methods is proposed. It is sufficient descent at each iteration without depending on the choice of the line search criterion. Under usual assumptions, and using the weak Wolfe line search criterion to yield its steplength, its strong convergence is proved. Finally, choosing a specific algorithm from this family to solve large-scale unconstrained optimization problems, image restorations and machine learning, the corresponding numerical results show that the new algorithm is promising. Mathematics Subject Classification (2020) 65K05 · 90C52 · 90C53 · 90C56