A Study of Indicators for Identifying Zero Variables in Interior-Point Methods

This study is concerned with constrained optimization problems where the only inequality constraints are nonnegativity constraints on the variables. In these problems, the ability to identify zero variables (binding constraints) early on in an iterative method is of considerable value and can be use...

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Bibliographic Details
Published in:SIAM review 1994-03, Vol.36 (1), p.45-72
Main Authors: El-Bakry, A. S., Tapia, R. A., Zhang, Y.
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Calculus of variations and optimal control
Ellipsoids
Exact sciences and technology
Indicator functions
Linear programming
Marital property
Mathematical analysis
Mathematics
Newtons method
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Research universities
Sciences and techniques of general use
Zero
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Summary:This study is concerned with constrained optimization problems where the only inequality constraints are nonnegativity constraints on the variables. In these problems, the ability to identify zero variables (binding constraints) early on in an iterative method is of considerable value and can be used to computational advantage. This work first gives a formal presentation of the notion of indicators for identifying zero variables, and then studies various indicators proposed in the literature for use with interior-point methods for linear programming. Both theory and experimentation are presented that speak strongly against the use of the variables as indicators; perhaps the most frequently used indicator in the literature. This study implies that an indicator proposed by Tapia is particularly effective in the context of primal-dual interior-point methods. The local rate of convergence for several indicators is also studied.
ISSN:0036-1445
1095-7200
DOI:10.1137/1036003