Some diagonal preconditioners for limited memory quasi-Newton method for large Scale optimization

One of the well-known methods in solving large scale unconstrained optimization is limited memory quasi-Newton (LMQN) method. This method is derived from a subproblem in low dimension so that the storage requirement as well as the computation cost can be reduced. In this paper, we propose a preconditioned LMQN method which is generally more effective than the LMQN method dueto the main defect of the LMQN method that it can be very slow on certain type of nonlinear problem such as ill-conditioned problems. In order to do this, we propose to use a diagonal updating matrix that has been derived based on the weak quasi-Newton relation to replace the identity matrix to approximate the initial inverse Hessian. The computational results show that the proposed preconditioned LMQN method performs better than LMQN method that without preconditioning.

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