A new truncated mixed spectrum conjugate gradient method

The conjugate gradient method has the advantages of small storage and fast computation, and has obvious advantages for solving large-scale problems. This article modifies the HS parameter based on the parameter types of the PRP class, while ensuring that the algorithm not only has good numerical performance, but also hopes to have good convergence properties of FR. A truncated mixed conjugation parameter was designed for this, and a new spectral conjugation parameter was designed based on this. This article proves that the algorithm has global convergence using strong Wolfe line search conditions. Finally, through numerical experiments on the problems in the CUTEr test set, it was found that the algorithm has better numerical performance compared to the other three types of methods.