# Updating lower bounds when using Karmarkar's projective algorithm for linear programming

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## Abstract

We give two results related to Gonzaga's recent paper showing that lower bounds derived from the Todd-Burrell update can be obtained by solving a one-variable linear programming problem involving the centering direction and the affine direction. We show how these results may be used to update the primal solution when using the dual affine variant of Karmarkar's algorithm. This leads to a dual projective algorithm.

## Key Words

Karmarkar's algorithm lower bounds linear programming interior-point methods## Preview

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## References

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## Copyright information

© Plenum Publishing Corporation 1993