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The implementation of linear programming algorithms based on homotopies

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Abstract

A fundamental homotopy-based linear programming algorithm, which utilizes Euler-predictor and Newton-corrector steps with restarts, is formulated and investigated numerically on problems representative of linear programs that arise in practice. A rich array of refinements of this basic algorithm are possible within the homotopy framework. Such refinements are needed in any practical implementation and are discussed in detail. Implications for the design of integrated large-scale mathematical programming software are also briefly considered.

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Authors and Affiliations

  1. Department of Pure and Applied Mathematics, Washington State University, 99164-3113, Pullman, WA, USA

    J. L. Nazareth

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  1. J. L. Nazareth
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Additional information

Communicated by N. Megiddo.

This research was supported by NSF Grant DMS-8815513, and first appeared, under the same title, as Technical Report 91-6 (October, 1991) issued by the department below.

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Nazareth, J.L. The implementation of linear programming algorithms based on homotopies. Algorithmica 15, 332–350 (1996). https://doi.org/10.1007/BF01961543

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  • DOI: https://doi.org/10.1007/BF01961543

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