New quasi-Newton methods via higher order tensor models (Q629502)

The authors propose a new quasi-Newton equation in nonlinear optimization by using the fourth order tensor model of the objective function. The modified equation is able to reduce the multiplier of the third order error term to 1/6 and to drop the fourth order error term, making a better approximation to the Hessian matrix. The global and local convergence of the proposed method is established. Some numerical results are presented to show that the effectiveness of the modified algorithm.