Three Term Conjugate Gradient Technique and its Global Convergence based on the Zhang, Zhou and Li methods

Abstract

The optimal conjugation coefficient distinguishes conjugate gradient methods such as two-term, three-term, and conditional from other descent methods. A novel conjugation parameter formula is constructed from Zhang, Zhou, and Li's well-known formula to formulate a three-term conjugation gradient method in the unconstrained optimization domain. The conjugation parameter  and the third term parameter were constructed by incorporating the Perry conjugation condition into Shanno's memory-free strategy of a conjugate gradient. The approach demonstrated a steeply sloped search direction for each iteration by demonstrating stability, global convergence, and sufficient descent analysis in the presence of a strong Wolf case. The empirical results established that the proposed method is more efficient than Zhang et al.'s techniques. Through the use of a collection of nonlinear mathematical functions.