An algorithm for solving large-scale nonlinear optimization problems with simple bounds is described. The algorithm is an $\ell_\infty$-norm trust-region method that uses both active set identification techniques as well as limited memory BFGS updating for the Hessian approximation. The trust-region subproblems are solved using primal-dual interior point techniques that exploit the structure of the limited memory Hessian approximation. A restart strategy ensures that the algorithm identifies the optimal constraints in finite number iterations under a standard nondegeneracy hypothesis. Local and global convergence properties are established, and the results of numerical tests are given.
University of Washington, Department of Mathematics Box 354350 Seattle, WA 98195-4350 07/09/07