A conjugate gradient algorithm without Lipchitz continuity and its applications

An improved conjugate gradient algorithm is proposed that does not rely on the line search rule and automatically achieves sufficient descent and trust region qualities. It is applicable to solve unconstrained problems and large-scale nonsmooth problems. Furthermore, it demonstrates global convergence properties without the need for Lipschitz continuity conditions. Numerical experiments on nonconvex unconstrained problems and large scale nonsmooth convex optimization problems demonstrate the effectiveness and efficiency of the proposed algorithm compared with the same structural algorithm. Finally, the new algorithm is applied to Muskingum model solving in engineering problems and image restoration, which shows the prospect of the new algorithm.