A New Modified Secant Condition for Non-linear Conjugate Gradient Methods with Global Convergence

The Conjugate Gradient Methods(CGM) are well-recognized techniques for handling nonlinear optimization problems. Dai and Liao (2001) employ the secant condition approach, this study utilizes the modified secant condition proposed by Yabe-Takano (2004) and Zhang and Xu (2001), which is satisfied at each iteration through the implementation of the strong Wolf-line search condition. Additionally, please provide three novel categories of conjugate gradient algorithms of this nature. We examined 15 well-known test functions. This novel approach utilises the existing gradient and function value to accurately approximate the goal function with high-order precision. The worldwide convergence of our novel algorithms is demonstrated under certain conditions. Numerical results are provided, and the efficiency is proven by comparing it to other approaches.