Computational Optimization and Applications

, Volume 35, Issue 2, pp 177–197 | Cite as

On Affine-Scaling Interior-Point Newton Methods for Nonlinear Minimization with Bound Constraints

Article

Abstract

A class of new affine-scaling interior-point Newton-type methods are considered for the solution of optimization problems with bound constraints. The methods are shown to be locally quadratically convergent under the strong second order sufficiency condition without assuming strict complementarity of the solution. The new methods differ from previous ones by Coleman and Li [Mathematical Programming, 67 (1994), pp. 189–224] and Heinkenschloss, Ulbrich, and Ulbrich [Mathematical Programming, 86 (1999), pp. 615–635] mainly in the choice of the scaling matrix. The scaling matrices used here have stronger smoothness properties and allow the application of standard results from non smooth analysis in order to obtain a relatively short and elegant local convergence result. An important tool for the definition of the new scaling matrices is the correct identification of the degenerate indices. Some illustrative numerical results with a comparison of the different scaling techniques are also included.

Keywords

Newton’s method affine scaling interior-point method quadratic convergence identification of active constraints 

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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and StatisticsUniversity of WürzburgWürzburgGermany

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