Global convergence of a two-parameter family of conjugate gradient methods without line search

We study the global convergence of a two-parameter family of conjugate gradient methods in which the line search procedure is replaced by a fixed formula of stepsize. This character is of significance if the line search is expensive in a particular application. In addition to the convergence results, we present computational results for various conjugate gradient methods without line search including those discussed by Sun and Zhang (Ann. Oper. Res. 103 (2001) 161–173).