**6. Conclusions**

The contributions of this work are two aspects. The one is to design a new computing schemes for the spectral parameter which ensures the *θk* > 1. The other is to propose a new computing method for the conjugate parameter. These two techniques such that the search directions always possess descent property independent of the line search technique. As a result, the presented JYJLL-SCGM possesses global convergence if using the Wolfe line search to yield the steplength. A lot of numerical experiments in comparison with relative methods show that our SCGM is promising.

As further works, we think the following two problems are interesting and worth studying. The one is to design new approaches for the spectral parameter to guarantee *θk* > 1, such as, combining the Newton direction and some new quasi-Newton equations, or the new conjugate conditions. The other is to find new computation techniques for the conjugate parameter with the help of the existing approaches, for example, the hybrid parameter, the three–term conjugate parameter et al.

**Author Contributions:** Conceptualization, J.J. and X.J.; methodology, J.J. and X.J.; formal analysis, L.Y. and P.L.; numerical experiments, L.Y. and P.L.; writing—original draft preparation, M.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by Natural Science Foundation of China under Grant No. 11771383, Natural Science Foundation of Guangxi Province under Grant No. 2016GXNSFAA380028, Research Foundation of Guangxi University for Nationalities under Grant No. 2018KJQD02, and Middle-aged and Young Teachers' Basic Ability Promotion Project of Guangxi Province under Grant No. 2017KY0537.

**Conflicts of Interest:** The authors declare no conflict of interest.
