An improved LS conjugate gradient method with Armijo search

Conjugate gradient method is an important method for solving unconstrained optimization problem.By taking a little modification to the search direction,an improved LS conjugate gradient method is proposed,which provides automatically a sufficient descent direction for the objective function at each iteration.If exact line search is used,the given method reduces to the standard LS method.Under mild conditions,the proposed method with Armijo line search converges globally even if the minimization function is nonconvex.Meanwhile,numerical results show that the algorithm is efficient.