Extra Quasi-Newton Equation for Unconstrained optimization

Abstract

Quasi-Newton equations play a central role in quasi-Newton methods for optimization and various quasi-Newton equations are available. The objective function’s third-order Taylor expansion has been used in this study to suggest a novel quasi-Newton equation. By adding more of the easily obtained values to the updated matrix, the goal is to enhance the accuracy of the Hessian (or its inverse) approximation. Under proper conditions, these methods are globally convergent for general functions and sometimes their numerical performance is superior to classical BFGS method. Modified versions of the quasi-Newton relation have recently been the focus of several papers with encouraging outcomes.