Paper Info
Title
A New Active Set Algorithm for Box Constrained Optimization
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.
Year
DOI
Venue
2006
10.1137/050635225
SIAM Journal on Optimization
Keywords
Field
DocType
unconstrained optimization step,nondegenerate stationary point,minpack-2 test problem library,cyclic bb method,cyclic barzilai-borwein,degenerate optimization,asa,unconstrained optimization,nonmonotone gradient projection step,box constrained optimization,gradient projection step,cg descent,conjugate gradient method,cbb,active set algorithm,conjugate gradient algorithm cg_descent,active set al- gorithm,nonmonotone gradient projection,stationary point,constrained optimization,second order,conjugate gradient
Gradient method,Convergence (routing),Conjugate gradient method,Mathematical optimization,Active set method,CUTEr,Degeneracy (mathematics),Stationary point,Mathematics,Constrained optimization
Journal
Volume
Issue
ISSN
17
2
1052-6234
Citations 
PageRank 
References 
74
2.89
36
Authors
2
Name
Order
Citations
PageRank
William W. Hager11603214.67
Hongchao Zhang280943.29