Convergence property of a class of variable metric methods Original Research Article

We investigate convergence property of the restricted Broyden class of variable metric methods. We show that when these methods with unit step are applied to a strictly convex quadratic objective function, the generated iterative sequence converges to the unique solution of the problem globally and superlinearly. Moreover, the distance between the iterative matrix and the Hessian matrix of the objective function decreases with iterations. The sequence of function values also exhibits descent property when the iteration is sufficiently large.