Global Convergence Properties of the Conjugate Descent Method with Armijo-type Line Searches

摘要

This paper investigates global convergence properties of the conjugate descent(GD) method. It is an important property that the strong Wolfe line search with σ < 1 can ensure descent direction at any iteration for the CD method. In this paper,we will propose two Armijo-type line searches. The CD method can also ensure all search directions downhill with the two Armijo-type line searches as well as with the strong Wolfe line search or generalized Wolf line search. Under the two Armijo-type line searches, the CD method is proved to convergence globally.