A New Diagonal Quasi-Newton Algorithm for Unconstrained Optimization Problems

Abstract This paper presents a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. The new method uses new criteria to generate the Hessian approximation to control the diagonal elements. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems show that the proposed method is superior to several certain diagonal methods.Mathematics subject classification 90C30 . 65K05