4. Conclusion

The conjugate gradient methods and trust region methods are very popular now. Many scientists consider these methods.

Namely, different modifications of these methods are made, with the aim to improve them.

Next, the scientists try to make not only new methods but also whole new classes of methods. For the specific values of the parameters, individual methods are distinguished from these classes. It is always more desirable to make a class of methods instead of individual methods.

Hybrid conjugate gradient methods are made in many different ways; this class of conjugate gradient methods is always actual.

Further, one of the contemporary trends is to use BFGS update in constructions of new conjugate gradient methods (e.g., see [46]).

Finally, let us emphasize that contemporary papers often use the Picard-Mann-Ishikawa iterative processes and they make the connection of these kinds of processes with the unconstrained optimization (see [29, 37, 38]).

Applied Mathematics
