Convergence of modified conjugate gradient methods without line search

Abstract

In this paper, a class of modified conjugate gradient methods are proposed, which have the following attractive properties: (1) the step length is determined by a formula; (2) the iterative direction is always a sufficient descent direction without utilizing the line search. Under the boundedness of the level set and the Lipschitz continuity of the underlying function, the proposed methods are global convergent. Some numerical results are given to illustrate the effectiveness of the proposed methods.