A novel limited memory method for solving large-scale bound constrained optimization problems is introduced. The new algorithm uses a combination of the steepest decent directions and quasi Newton directions in a new schema to identify the optimal active bound constraints. The quasi Newton directions are computed using limited memory SR1 matrices. As it is known, the SR1 matrices are not necessarily positive definite, consequently, the quasi-Newton direction need not be a descent direction. In such a case, we regularize this direction so that it will become a descent direction. After the set of optimal active variables are identified, the algorithm uses a combination of limited memory quasi Newton method and conjugate gradient method to explore the subspace of free variables. The convergence theory of the algorithm is also provided. At the end, numerical results of the algorithm applied to a list of bound constrained problems from the CUTEr library and comparisons with two state-of-the-art bound constrained solvers (L-BFGS-B, ASA-CG) are demonstrated. |