A HYBRID MBFGS AND CBFGS METHOD FOR NONCONVEX MINIMIZATION WITH A GLOBAL COMPLEXITY BOUND

We present a BFGS type method for solving the unconstrained optimization problem, which is a combination of the MBFGS method and the CBFGS method proposed by Li and Fukushima in [4, 5]. This hybrid scheme sufficiently utilizes advantages of both methods, that is, it not only reduces to the standard BFGS method for local strongly convex functions finally but also regularizes nonconvex functions in the singular case. We show that the proposed method converges globally and superlinearly. Moreover, we investigate a global complexity bound for this method, which is O(epsilon(-2)). Some preliminary numerical results are also reported.