language: en

Trust-region interior-point algorithms for minimization problems with simple bounds

J. E. Dennis and Lus N. Vicente

Abstract Two trust-region interior-point algorithms for the solution of minimization problems with simple bounds are presented. The algorithms scale the local model in a way proposed by Coleman and Li [1], but they are new otherwise. 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 first-order 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 the second algorithm are presented.

Keywords. trust-region methods, interior-point algorithms, Dikin-Karmarkar ellipsoid, Coleman and Li scaling, simple bounds. AMS subject classification. 49M37, 90C20, 90C30

1 Introduction