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Operations Research ’91 pp 126–128Cite as

Estimating the Complexity of Path-Following Methods for Linear Programming by Curvature Integrals

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Abstract

In this work we study the complexity of certain interior point methods, which rapidly developed since Karmarkar published his work 1984, for solving a linear program and its dual

$$\begin{gathered} \mathop {\min }\limits_x {c^T}x \mathop {\max }\limits_{y,s} {b^T}y \hfill \\ Ax = b \left( {LP} \right), {A^T}y + s = c \left( {LD} \right) \hfill \\ x \geqslant 0 s \geqslant 0. \hfill \\ \end{gathered}$$

Here A is. an m × n-matrix, c is an n-vector and b is an m-vector. Let z:= (x,s,y).

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References

  1. N. Karmarkar, Riemannian geometry underlying interior point methods, Mathematical Developments Arising from Linear Programming (J.C. Lagarias and M.J. Todd. Eds.), Contemporary Mathematics, Vol. 114, Amer. Math. Soc. 1990, pp. 51–76.

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  2. G. Sonnevend, J. Stoer and G. Zhao, On the complexity of following the central path of linear programs by linear extrapolation II, presented at the International Symposium: Interior Point Methods for Linear Programming (the Netherlands, 1990), to appear in: Math. Progr. series B (eds. C. Roos and J.-P. Vial).

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  3. G. Zhao and J. Stoer, Estimating the complexity of path-following methods for solving linear programs by curvature integrals, report No. 225, Schwerpunktpro-gram Anwendungsbezogene Optimierung und Steuerung. Inst. für Ang. Math. und Statistik, Universität Würzburg (1990), to appear in Appl. Math. & Optimization.

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik und Statistik, Universität Würzburg, Am Hubland, D-8700, Würzburg, Germany

    Gongyun Zhao

Authors
  1. Gongyun Zhao
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Editors and Affiliations

  1. FB IV, Mathematik, Universität Trier, Postfach 38 25, D-5500, Trier, Germany

    Peter Gritzmann , Rainer Hettich , Reiner Horst  & Ekkehard Sachs , ,  & 

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© 1992 Physica-Verlag Heidelberg

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Zhao, G. (1992). Estimating the Complexity of Path-Following Methods for Linear Programming by Curvature Integrals. In: Gritzmann, P., Hettich, R., Horst, R., Sachs, E. (eds) Operations Research ’91. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-48417-9_36

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  • DOI: https://doi.org/10.1007/978-3-642-48417-9_36

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-7908-0608-3

  • Online ISBN: 978-3-642-48417-9

  • eBook Packages: Springer Book Archive

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