New accelerated nonlinear conjugate gradient algorithms which are mainly modifications of the Dai and Yuan’s for unconstrained optimization are proposed. Using the exact line search, the algorithm reduces to the Dai and Yuan conjugate gradient computational scheme. For inexact line search the algorithm satisfies the sufficient descent condition. Since the step lengths in conjugate gradient algo...

Two nonlinear conjugate gradient-type methods for solving unconstrained optimization problems are proposed. An attractive property of the methods, is that, without any line search, the generated directions always descend. Under some mild conditions, global convergence results for both methods are established. Preliminary numerical results show that these proposed methods are promising, and comp...

We propose a generalization of the conjugate gradient method that uses multiple preconditioners, combining them automatically in an optimal way. The derivation is described in detail, and analytical observations are made. A short recurrence relation does not hold in general for this new method, but in at least one case such a relation is satisfied: for two symmetric positive definite preconditi...

In this paper, We propose a new nonlinear conjugate gradient method (FRA) that satisfies sufficient descent condition and global convergence under the inexact line search of strong wolf powell. Our numerical experiment shaw efficiency in solving set problems from CUTEst package, proposed formula gives excellent results at CPU time, number iterations, ratings when compared to WYL, DY, PRP, FR me...