On the New Quasi-Newton Equation for Unconstrained Optimization

Quasi-Newton methods (QN) are very useful in finding the optimal solution to the unconstrained optimization problems. The updated Hessian approximations fulfill the equation on each iteration for solving unconstrained optimization problems, hence the quasi-Newton equation is commonly used as the foundation of quasi-Newton algorithms. We propose and examine a novel quasi-Newton technique and its implementation in this research, which uses cubic interpolation to generate a new quasi-Newton equation. Our updates have been proved to produce positive definite matrices when appropriate assumptions are made. The improved BFGS approach has been shown to have global convergence. Comparing the suggested formula to the BFGS method, numerical results reveal that it is better and more efficient.