Abstract:

 A modified DY conjugate gradient method(MDY)is proposed based on DY method and HZ method. This method can generate sufficient descent directions for the objective functions, and this property is independent of the line search method used. Under mild conditions, it is proved that the conservative MDY method with Armijo line search or Wolfe line search converges globally even if the minimization function is nonconvex. Numerical results show that the proposed method is efficient.

Key words:  sufficient descent; DY method; armijo line search; wolfe line search; global convergence