Global convergence of the Dai-Yuan conjugate gradient method with perturbations

In this paper, the authors propose a class of Dai-Yuan (abbr. DY) conjugate gradient methods with linesearch in the presence of perturbations on general function and uniformly convex function respectively. Their iterate formula is x _k+1 = x _k + α _k (s _k + ω _k ), where the main direction s _k is obtained by DY conjugate gradient method, ω _k is perturbation term, and stepsize α _k is determined by linesearch which does not tend to zero in the limit necessarily. The authors prove the global convergence of these methods under mild conditions. Preliminary computational experience is also reported.