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Implementation of an interior point method with basis preconditioning
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DOI：10.1007/s12532-020-00181-8.png)
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Abstract
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The implementation of a linear programming interior point solver is described that is based on iterative linear algebra. The linear systems are preconditioned by a basis matrix, which is updated from one interior point iteration to the next to bound the entries in a certain tableau matrix. The update scheme is based on simplex-type pivot operations and is implemented using linear algebra techniques from the revised simplex method. An initial basis is constructed by a crash procedure after a few interior point iterations. The basis at the end of the interior point solve provides the starting basis for a crossover method which recovers a basic solution to the linear program. Results of a computational study on a diverse set of medium to large-scale problems are discussed.
Keywords:
Linear programming
Interior point methods
Basis preconditioning
Crossover
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