On Central-Path Proximity Measures in Interior-Point Methods |
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Authors: | M D Gonzalez-Lima C Roos |
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Institution: | (1) Computing Scientific Department and Center for Statistics and Mathematical Software (CESMa), Computing and Mathematical Sciences Department, Simón Bolívar University, Texas A&M University of Corpus Christi, Caracas, Corpus Christi, Venezuela, Texas, USA;(2) Department of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, Netherlands |
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Abstract: | One of the main ingredients of interior-point methods is the generation of iterates in a neighborhood of the central path.
Measuring how close the iterates are to the central path is an important aspect of such methods and it is accomplished by
using proximity measure functions. In this paper, we propose a unified presentation of the proximity measures and a study
of their relationships and computational role when using a generic primal-dual interior-point method for computing the analytic
center for a standard linear optimization problem. We demonstrate that the choice of the proximity measure can affect greatly
the performance of the method. It is shown that we may be able to choose the algorithmic parameters and the central-path neighborhood
radius (size) in such a way to obtain comparable results for several measures. We discuss briefly how to relate some of these
results to nonlinear programming problems.
The first author was partially supported by Simón Bolívar University, Venezuelan National Council for Sciences and Technology
(CONICIT) Grant PG97-000592, Center for Research on Parallel Computing of Rice University, and TU Delft. The authors thank
Amr El Bakry, Richard Tapia, Adolfo Quiroz, and Pedro Berrizbeitia for discussions and suggestions. They acknowledge the observations
and comments of the editors and an anonymous referee. |
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Keywords: | Primal-dual interior-point methods central path proximity measures |
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