A new diagonal quasi-Newton algorithm for unconstrained optimization problems

We present a new diagonal quasi-Newton method for solving unconstrained optimization problems based on the weak secant equation. To control the diagonal elements, the new method uses new criteria to generate the Hessian approximation. We establish the global convergence of the proposed method with the Armijo line search. Numerical results on a collection of standard test problems demonstrate the superiority of the proposed method over several existing diagonal methods.