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

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Entry Submitted: 07/11/2007
Entry Accepted: 07/11/2007
Entry Last Modified: 07/11/2007

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