Nonmonotone conjugate gradient algorithm without gradient Lipschitz continuity for nonconvex minimizations

For this article, a nonmonotone nonlinear gradient method framework is designed for nonconvex optimization problems. Using two classical nonmonotone line search techniques, the global convergence is proven, and we do not need the assumption that the gradient is Lipschitz continuous. Furthermore, a specific nonlinear gradient method using the Hardmar product instead of the normal inner product is designed, which has sufficient descent features with no need for line search technology. Numerical experiments in engineering problems and colour image restoration indicate that the specific nonlinear gradient algorithm is comparable with other analogous nonlinear gradient algorithms.