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Effective Finite Termination Procedures in Interior-Point Methods for Linear Programming (1998)
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| Citations: | 3 - 1 self |
BibTeX
@MISC{Williams98effectivefinite,
author = {Pamela Joy Williams},
title = {Effective Finite Termination Procedures in Interior-Point Methods for Linear Programming},
year = {1998}
}
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Abstract
Due to the structure of the solution set an exact solution to... bounds are incorporated into the model to prevent the computed solution from violating the bound constraints. Theory in the literature is extended to the new model. Empirical evidence shows that the proposed model reduces the number of projection attempts needed to find an exact solution. When early termination is the goal, projection from a pure composite Newton step is advocated. However, the cost may exceed the benefits due to the average need of more than one projection attempt to find an exact solution. Variants of Mehrotra's predictor-corrector primal-dual interior-point algorithm provide the foundation for most practical interior-point codes. To take advantage of all available algorithmic information, we investigate the behavior of the Tapia predictor-corrector indicator, which incorporates the corrector step, to identify the optimal partition. Globally, the Tapia predictor-corrector indicator behaves poorly as do all indicators, but locally exhibits fast convergence.
Keyphrases
linear programming effective finite termination procedure exact solution interior-point method tapia predictor-corrector indicator projection attempt available algorithmic information average need practical interior-point code computed solution empirical evidence show optimal partition early termination pure composite newton step new model fast convergence predictor-corrector primal-dual interior-point algorithm corrector step bound constraint
