A modified scaled conjugate gradient method with global convergence for nonconvex functions

Following Andrei's approach, a modified scaled memoryless BFGS preconditioned conjugate gradient method is proposed based on the modified secant equation suggested by Li and Fukushima. It is shown that the method is globally convergent without convexity assumption on the objective function. Furthermore, for uniformly convex objective functions, sufficient descent property of the method is established based on an eigenvalue analysis. Numerical experiments are employed to demonstrate the efficiency of the method.