CRPC-TR94478-S: Trust-Region Interior-Point Algorithms for
Minimization Problems with Simple Bounds

John Dennis, Luis Vicente

September, 1994 (Revised: June, 1995)

Two trust--region interior--point algorithms for the solution of
minimization problems with simple bounds are analyzed and tested. The
algorithms scale the local model in a way similar to Coleman and Li
[1].  The first algorithm is more usual in that the trust region and
the local quadratic model are consistently scaled. The second
algorithm proposed here uses an unscaled trust region.  A global
convergence result for these algorithms is given and dogleg and
conjugate--gradient algorithms to compute trial steps are
introduced. Some numerical examples that show the advantages of the
second algorithm are presented.