Memory Quasi - Newton Algorithm forLarge - Scale Nonlinear Bound Constrained

In this paper we propose a subspace limited memory quasi-Newton method for solving large-scale optimization with simple bounds on the variables. The limited memory quasi-Newton method is used to update the variables with indices outside of the active set, while the projected gradient method is used to update the active variables. The search direction consists of three parts: a subspace quasi-Newton direction, and two subspace gradient and modiied gradient directions. Our algorithm can be applied to large-scale problems as there is no need to solve any subproblems. The global convergence of the method is proved and some numerical results are also given.