Advertisement

Interior-Point Methods for Linear Optimization

  • Wilhelm Forst
  • Dieter Hoffmann
Chapter
Part of the Springer Undergraduate Texts in Mathematics and Technology book series (SUMAT)

Abstarct

The development of the last 30 years has been greatly influenced by the aftermath of a “scientific earthquake” which was triggered in 1979 by the findings of the Russian mathematician Khachiyan (1952–2005) and in 1984 by those of the Indian-born mathematician Karmarkar. The New York Times, which profiled Khachiyan’s achievement in a November 1979 article entitled “Soviet Mathematician Is Obscure No More,” called him “the mystery author of a new mathematical theorem that has rocked the world of computer analysis.”

Keywords

Dual Problem Primal Problem Feasible Point Linear Optimization Central Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Fi/Co.
    A. Fiacco, G. McCormick (1990): Nonlinear Programming — Sequential Unconstrained Minimization Techniques. SIAM, PhiladelphiaMATHGoogle Scholar
  2. Son.
    G. Sonnevend (1986): An ‘Analytical Center’ for Polyhedrons and New Classes of Global Algorithms for Linear (Smooth, Convex) Programming. Lecture Notes in Control and Information Sciences 84. Springer, Berlin, Heidelberg, New York, pp. 866–875Google Scholar
  3. MTY.
    S. Mizuno, M. J. Todd, Y. Ye (1993): On Adaptive-Step Primal-Dual Interior-Point Algorithms for Linear Programming. Mathematics of Operations Research 18, pp. 964–981MATHCrossRefMathSciNetGoogle Scholar
  4. Ca/Ma.
    V. Candela, A. Marquina (1990): Recurrence Relations for Rational Cubic Methods II: The Chebyshev Method. Computing 45, pp. 355–367MATHCrossRefMathSciNetGoogle Scholar
  5. RTV.
    C. Roos, T. Terlaky, J. P. Vial (2005): Interior Point Methods for Linear Optimization. Springer, Berlin, Heidelberg, New YorkGoogle Scholar
  6. Meh.
    S. Mehrotra (1992): On the Implementation of a Primal-Dual Interior-Point Method. SIAM J. Optimization 2, pp. 575–601Google Scholar
  7. No/Wr.
    J. Nocedal, S. J. Wright (2006): Numerical Optimization. Springer, Berlin, Heidelberg, New YorkMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Fak. Mathematik und Wirtschaftswissenschaften Inst. Numerische MathematikUniversität UlmUlmGermany
  2. 2.FB Mathematik und StatistikUniversität KonstanzKonstanzGermany

Personalised recommendations