Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming

Adaptive use of iterative methods in predictor–corrector interior point methods for linear programming

0.00 Avg rating0 Votes
Article ID: iaor20023469
Country: United States
Volume: 25
Issue: 1/4
Start Page Number: 387
End Page Number: 406
Publication Date: Jan 2000
Journal: Numerical Algorithms
Authors: ,
Keywords: interior point methods
Abstract:

In this work we devise efficient algorithms for finding the search directions for interior point method applied to linear programming problems. There are two innovations. The first is the use of updating of preconditioners computed for previous barrier parameters. The second is an adaptive automated procedure for determining whether to use a direct or iterative solver, whether to reinitialize or update the preconditioner, and how many updates to apply. These decisions are based on predictions of the cost of using the different solvers to determine the next search direction, given costs in determining earlier directions. We summarize earlier results using a modified version of the OBI-R code of Lustig, Marsten, and Shanno, and we present results from a predictor–corrector code PCx modified to use adaptive iteration. If a direct method is appropriate for the problem, then our procedure chooses it, but when an iterative procedure is helpful, substantial gains in efficiency can be obtained.

Reviews

Required fields are marked *. Your email address will not be published.