SECEIVED F€B 2 8 19% An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is baaed on the gradient projection method and uses a limikd-memory BFGS matrix to appraximak the Hessian of the objective function. We show how to take advantage of the form of the limited-memory approximation t a implement the algorithm efficiently. The remits of numerical tests on a set of large problems are reported.

SECEIVED F€B 2 8 19% An algorithm for solving large nonlinear optimization problems with simple bounds is described. It is baaed on the gradient projection method and uses a limikd-memory BFGS matrix to appraximak the Hessian of the objective function. We show how to take advantage of the form of the limited-memory approximation t a implement the algorithm efficiently. The remits of numerical tests on a set of large problems are reported.

L-BFGS-B is a limited-memory algorithm for solving large nonlinear optimization problems subject to simple bounds on the variables. It is intended for problems in which information on the Hessian matrix is difficult to obtain, or for large dense problems. L-BFGS-B can also be used for unconstrained problems and in this case performs similarly to its predessor, algorithm L-BFGS (Harwell routine VA15). The algorithm is implemented in Fortran 77.

An algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints is described. It applies sequential quadratic programming techniques to a sequence of barrier problems, and uses trust regions to ensure the robustness of the iteration and to allow the direct use of second order derivatives. This framework permits primal and primal-dual steps, but the paper focuses on the primal version of the new algorithm. An analysis of the convergence properties of this method is presented.

The design and implementation of a new algorithm for solving large nonlinear programming problems is described. It follows a barrier approach that employs sequential quadratic programming and trust regions to solve the subproblems occurring in the iteration. Both primal and primal-dual versions of the algorithm are developed, and their performance is illustrated in a set of numerical tests.