Convergence rate of primal dual reciprocal Barrier Newton interior-point methods
作者:
AmrS. El-Bakry,
期刊:
Optimization Methods and Software
(Taylor Available online 1998)
卷期:
Volume 9,
issue 1-3
页码: 37-44
ISSN:1055-6788
年代: 1998
DOI:10.1080/10556789808805685
出版商: Gordon and Breach Science Publishers
关键词: Convergence Rate;Interior-Point Methods;Reciprocal Barrier Function
数据来源: Taylor
摘要:
Primal-dual interior-point methods for linear programming are often motivated by a certaijn nonlinear transformation of the Karush-Kuhn-Tucker conditions of the logarithmic Barrier formulation. Recently, Nassar [5] studied the reciprocal Barrier function formulation of the problem. Using a similar nonlinear transformation, he proved local convergence fir Newton interior-point method on the resulting perturbed Karush-Kuhn-Tucker systerp. This result poses the question whether this method can exhibit fast convergence ral[e for linear programming. In this paper we prove that, for linear programming, Newton's method on the reciprocal Barrier formulation exhibits at best Q-linear convergence rattf. Moreover, an exact Q1factor is established which precludes fast linear convergence
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