A compact limited memory method for large scale unconstrained optimization

A compact limited memory method for solving large scale unconstrained optimization problems is proposed. The compact representation of the quasi-Newton updating matrix is derived to the use in the form of limited memory update in which the vector yk is replaced by a modified vector yˆk so that more available information about the function can be employed to increase the accuracy of Hessian approximations. The global convergence of the proposed method is proved. Numerical tests on commonly used large scale test problems indicate that the proposed compact limited memory method is competitive and efficient.