A New Active Set Algorithm for Box Constrained Optimization

Authors:
William W. Hager;Hongchao Zhang
Affiliations:
-;-
Venue:
SIAM Journal on Optimization
Year:
2006

Citing 0
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Abstract

An active set algorithm (ASA) for box constrained optimization is developed. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for branching between the two steps. Global convergence to a stationary point is established. For a nondegenerate stationary point, the algorithm eventually reduces to unconstrained optimization without restarts. Similarly, for a degenerate stationary point, where the strong second-order sufficient optimality condition holds, the algorithm eventually reduces to unconstrained optimization without restarts. A specific implementation of the ASA is given which exploits the recently developed cyclic Barzilai-Borwein (CBB) algorithm for the gradient projection step and the recently developed conjugate gradient algorithm CG_DESCENT for unconstrained optimization. Numerical experiments are presented using box constrained problems in the CUTEr and MINPACK-2 test problem libraries.