Recently, Yu and Guan proposed a modified PRP method (called DPRP method) which can generate sufficient descent directions for the objective function. They established the global convergence of the DPRP method based on the assumption that stepsize is bounded away from zero. In this paper, without the requirement of the positive lower bound of the stepsize, we prove that the DPRP method is globally convergent with a modified strong Wolfe line search. Moreover, we establish the global convergence of the DPRP method with a Armijo-type line search. The numerical results show that the proposed algorithms are efficient. Mathematical subject classification: Primary: 90C30; Secondary: 65K05.
PRP method; sufficient descent property; modified strong Wolfe line search; Armijo-type line search; global convergence
