Global convergence of a modified CG-based method with Lipschitz continuity for unconstrained optimization and image restoration problems

Abstract

In this study, we extend the recently proposed RMIL* method to construct a new three-term conjugate gradient (TTCG) direction and show that it possesses sufficient descent property independently of the line search strategy used. We further prove the global convergence of the method using the famous Wolfe line search conditions. The computational efficiency of the algorithm (method) is tested on a set of unconstrained optimization and image restoration problems. The Findings of the numerical experiments show that the proposed method is robust and promising for both unconstrained minimization and application problems.