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. Hager | 1 | 1603 | 214.67 |
Hongchao Zhang | 2 | 809 | 43.29 |