This paper presents a limited-memory quasi-Newton algorithm for solving large nonlinear optimization problems with simple bounds. The algorithm uses a limited-memory BFGS matrix to approximate the Hessian of the objective function, which allows for efficient implementation. The method is based on the gradient projection approach to determine active constraints at each iteration and employs line searches instead of trust regions. The paper outlines the algorithm, including the computation of the generalized Cauchy point and subspace minimization, and discusses the efficiency of different methods for subspace minimization. Numerical experiments comparing the new algorithm with LANCELOT's SUBMIN subroutine show that the dual method is generally the fastest, while the direct primal method is competitive. The new algorithm is efficient in terms of computational cost per iteration and storage requirements, making it suitable for solving large, dense problems where the Hessian is unavailable.This paper presents a limited-memory quasi-Newton algorithm for solving large nonlinear optimization problems with simple bounds. The algorithm uses a limited-memory BFGS matrix to approximate the Hessian of the objective function, which allows for efficient implementation. The method is based on the gradient projection approach to determine active constraints at each iteration and employs line searches instead of trust regions. The paper outlines the algorithm, including the computation of the generalized Cauchy point and subspace minimization, and discusses the efficiency of different methods for subspace minimization. Numerical experiments comparing the new algorithm with LANCELOT's SUBMIN subroutine show that the dual method is generally the fastest, while the direct primal method is competitive. The new algorithm is efficient in terms of computational cost per iteration and storage requirements, making it suitable for solving large, dense problems where the Hessian is unavailable.