On free variables in interior point methods*
作者:
Csaba Mészáros,
期刊:
Optimization Methods and Software
(Taylor Available online 1998)
卷期:
Volume 9,
issue 1-3
页码: 121-139
ISSN:1055-6788
年代: 1998
DOI:10.1080/10556789808805689
出版商: Gordon and Breach Science Publishers
关键词: Constrained Optimization;Interior Point Methods
数据来源: Taylor
摘要:
Interior point methods, especially the algorithms for linear programming problems are sensitive if there are unconstrained (free) variables in the problem. While replacing a free variable by two nonnegative ones may cause numerical instabilities, the implicit handling results in a semidefinite scaling matrix at each interior point iteration. In the paper we investigate the effects if the scaling matrix is regularized. Our analysis will prove that the effect of the regularization can be easily monitored and corrected if necessary. We describe the regularization scheme mainly for the efficient handling of free variables, but a similar analysis can be made for the case, when the small scaling factors are raised to larger values to improve the numerical stability of the systems that define the searcn direction. We will show the superiority of our approach over the variable replacement method on a set of test problems arising from water management application
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