Global convergence of a special case of the Dai‐Yuan family without line search

Conjugate gradient methods are efficient to minimize differentiable objective functions in large dimension spaces. Recently, Dai and Yuan introduced a tree-parameter family of nonlinear conjugate gradient methods and show their convergence. However, line search strategies usually bring computational burden. To overcome this problem, in this paper, we study the global convergence of a special case of three-parameter family(the CD-DY family) in which the line search procedures are replaced by fixed formulae of stepsize.