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Infeasible-Interior-Point Algorithms

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Interior Point Methods of Mathematical Programming

Part of the book series: Applied Optimization ((APOP,volume 5))

Abstract

An interior-point algorithm whose initial point is not restricted to a feasible point is called an infeasible-interior-point algorithm. The algorithm directly solves a given linear programming problem without using any artificial problem. So the algorithm has a big advantage of implementation over a feasible-interior-point algorithm, which has to start from a feasible point. We introduce a primal-dual infeasible-interior-point algorithm and prove global convergence of the algorithm. When all the data of the linear programming problem are integers, the algorithm terminates in polynomial-time under some moderate conditions of the initial point. We also introduce a predictor-corrector infeasible-interior-point algorithm, which achieves better complexity and has superlinearly convergence.

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Author information

Authors and Affiliations

  1. Department of Prediction and Control, The Institute of Statistical Mathematics, Minato-ku, Tokyo, Japan, 106

    Shinji Mizuno

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  1. Shinji Mizuno
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Editor information

Editors and Affiliations

  1. Delft University of Technology, The Netherlands

    Tamás Terlaky

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© 1996 Kluwer Academic Publishers

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Mizuno, S. (1996). Infeasible-Interior-Point Algorithms. In: Terlaky, T. (eds) Interior Point Methods of Mathematical Programming. Applied Optimization, vol 5. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3449-1_5

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  • DOI: https://doi.org/10.1007/978-1-4613-3449-1_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3451-4

  • Online ISBN: 978-1-4613-3449-1

  • eBook Packages: Springer Book Archive

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