Postponing the Choice of Penalty Parameter and Step Length

We study, in the context of interior-point methods for linear programming, some possible advantages of postponing the choice of the penalty parameter and the steplength, which happens both when we apply Newton's method to the Karush-Kuhn-Tucker system and when we apply a predictor-corrector sch...

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Bibliographic Details
Published in:Computational optimization and applications 2003-01, Vol.24 (1), p.63-81
Main Authors: Villas-Boas, Fernando R, Perin, Clovis
Format: Article
Language:English
Subjects:
Algorithms
Linear programming
Mathematical models
Methods
Optimization
Online Access:Get full text
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Summary:We study, in the context of interior-point methods for linear programming, some possible advantages of postponing the choice of the penalty parameter and the steplength, which happens both when we apply Newton's method to the Karush-Kuhn-Tucker system and when we apply a predictor-corrector scheme. We show that for a Newton or a strictly predictor step the next iterate can be expressed as a linear function of the penalty parameter [mu], and, in the case of a predictor-corrector step, as a quadratic function of [mu]. We also show that this parameterization is useful to guarantee either the non-negativity of the next iterate or the proximity to the central path. Initial computational results of these strategies are shown and compared with PCx, an implementation of Mehotra's predictor-corrector method. [PUBLICATION ABSTRACT]
ISSN:0926-6003
1573-2894
DOI:10.1023/A:1021850032714