The following nonlinear programming problem with simple bounds on variables
is considered. The objective function is assumed to be twice continuously differentiable, and are given bound vectors in , and is the number of variables, which is assumed to be large.
The given subspace limited memory quasi-Newton algorithm does not need to solve any subproblems. The search direction of the algorithm consists of three parts: a subspace quasi-Newton direction, and two subspace gradient and modified gradient directions. The global convergence of the method is proved and some numerical results are given.