The convergence properties of some new conjugate gradient methods

In this paper, a new conjugate gradient formula βk∗ is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with some line searches such as the exact line search, the Wolfe–Powell line search and the Grippo–Lucidi line search are discussed. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula βk∗⩾0, and has the similar form with βkPRP. Preliminary numerical results show that the proposed methods are efficient.