A Novel Three Term Conjugate Gradient Method for Unconstrained Optimization via Shifted Variable Metric Approach with Application

Conjugate gradient (CG) methods embody a category of unconstrained optimization algorithms which are known to be of low memory requirements and possess the global convergence properties. In this chapter, we present a novel three term (CG) method based on the idea of the shifted variable metric approach. Under certain conditions, the global convergence result of the proposed method is demonstrated and numerical result have shown that the new method outperforms other methods in comparison based on some benchmark optimization test functions. However, we present the application of the new method on a problem of inflation rate in Nigeria from 2010 to 2018. The outcome has shown that the new method has relatively less error and can surely surrogate an LSM in regression analysis. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.