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Search directions for interior linear-programming methods

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Abstract

Since Karmarkar published his algorithm for linear programming, several different interior directions have been proposed and much effort was spent on the problem transformations needed to apply these new techniques. This paper examines several search directions in a common framework that does not need any problem transformation. These directions prove to be combinations of two problem-dependent vectors, and can all be improved by a bidirectional search procedure.

We conclude that there are essentially two polynomial algorithms: Karmarkar's method and the algorithm that follows a central trajectory, and they differ only in a choice of parameters (respectively lower bound and penalty multiplier).

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California, 94720, Berkeley, CA, USA

    Clovis C. Gonzaga

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  1. Clovis C. Gonzaga
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Additional information

Communicated by Nimrod Megiddo.

Research partly sponsored by CNPq-Brazilian National Council for Scientific and Technological Development, by National Science Foundation Grant ECS-8121149, Office of Naval Research Contract N00014-83-K-0602, AFOSR Grant 83-0361, State of California Microelectronics Innovation and Computer Research Opportunities Program, and General Electric.

On leave from COPPE-Federal University of Rio de Janeiro, Cx. Postal 68511, 21941 Rio de Janeiro, RJ, Brasil.

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Gonzaga, C.C. Search directions for interior linear-programming methods. Algorithmica 6, 153–181 (1991). https://doi.org/10.1007/BF01759039

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  • DOI: https://doi.org/10.1007/BF01759039

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