Global convergence of a two-parameter family of conjugate gradient methods without line search (Q697544)

In the implementation of a conjugate gradient (CG) method the stepsize is often determined by certain line search conditions which may become a significant burden for large-scale problems. To overcome this difficulty the authors 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 the stepsize and prove the main global convergence properties of CG methods without line search. Finally, some numerical experiments of CG methods with and without line search are presented. The computational results show that the methods without line search can be as effective as those with line search.