A Filter Diagonal Quasi-Newton Method with Weak Secant Equation

Based on the weak secant equation, a filter diagonal quasi-Newton method for minimizing unconstrained optimization is proposed. This method restricts the approximation of Hessian matrix to a diagonal matrix. If the trial step is monotone or can be accepted by the filter, the algorithm requires no line searches. Under some reasonable assumptions, the new algorithm is globally convergent. Preliminary numerical experiments are presented and show that the new algorithm is efficient and robust.