- ASTRAL: An Active Set $l_\infty$-Trust-Region Algorithm for Box Constrained Optimization Liang Xu(lxumath.washington.edu) James V. Burke(burkemath.washington.edu) Abstract: 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. Keywords: trust-region, L-BFGS, box constrained, large-scale Category 1: Nonlinear Optimization (Bound-constrained Optimization ) Citation: University of Washington, Department of Mathematics Box 354350 Seattle, WA 98195-4350 07/09/07 Download: [PDF]Entry Submitted: 07/11/2007Entry Accepted: 07/11/2007Entry Last Modified: 07/11/2007Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.