Convergence Rate of Greedy SR1 With Trust Region Method

Recently, Greedy Quasi-Newton methods have attracted wide interests of some researchers for their explicit superlinear convergence rate. These algorithms which achieve rapid local convergence construct a matrix sequence to approximate the Hessian matrix of the objective function iteratively. This paper proposes an algorithm, GR-SR1-TR, which incorporate Greedy SR1 method with Trust Region framework and employs a new correction technique. We prove that the approximation matrix sequence has a linear descent property under the Frobenius-norm metric. Further, both the global convergence and an explicit superlinear rate are established. The effectiveness of GR-SR1-TR has been verified by preliminary numerical experiments.