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Optimal ellipsoidal approximations around the Analytic center

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Abstract

We present a simple and self-contained proof for two-sided ellipsoidal approximations of certain convex setsS. The ellipsoids are centered at the minimum of the logarithmic barrier function forS. The ratio of inner and outer ellipsoid is optimal with respect to a self-concordance parameterθ.

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References

  1. Boyd S, Ghaoui LE (1993) Method of centers for minimizing generalized eigenvalues, Linear Algebra Appl, 188/189:63–111

    Google Scholar 

  2. Den Hertog D, Jarre F, Roos C, Terlaky T (1992) A unifying investigation of interior-point methods for convex programming, Technical Report, to appear in Math Programming, Ser B

  3. Jarre F (1989) The method of analytic centers for solving smooth convex programs, in Dolecki S (ed), Optimization, Lecture Notes in Mathematics, Vol 1405, Springer-Verlag, Berlin, pp 69–85

    Google Scholar 

  4. Jarre F (1992) Interior-point methods for convex programming, Appl Math Optim 26:287–311

    Google Scholar 

  5. Knobloch HW, Kappel F (1974) Gewöhnliche Differentialgleichungen, Teubner-Verlag, Stuttgart

    Google Scholar 

  6. Nesterov JE, Nemirovsky AS (1988) A general approach to polynomial-time algorithms design for convex programming, Report, Central Economical and Mathematical Institute, Academy of Sciences of the USSR, Moscow

    Google Scholar 

  7. Nesterov JE, Nemirovsky AS (1989) Self-concordant functions and polynomial-time methods in convex programming, Report, Central Economical and Mathematical Institute, Academy of Sciences of the USSR, Moscow

    Google Scholar 

  8. Sonnevend G (1986) An “Analytical Centre” for Polyhedrons and New Classes of Global Algorithms for Linear (Smooth, Convex) Programming, Lecture Notes in Control and Information Sciences, Vol 84, Springer-Verlag, Berlin, pp 866–878

    Google Scholar 

  9. Sonnevend G, Stoer J (1989) Global ellipsoidal approximations and homotopy methods for solving convex analytic programs, Appl Math Optim 21:139–166

    Google Scholar 

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Am Hubland, University of Würzburg, 97074, Würzburg, Germany

    F. Jarre

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  1. F. Jarre
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Communicated by J. Stoer

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Jarre, F. Optimal ellipsoidal approximations around the Analytic center. Appl Math Optim 30, 15–19 (1994). https://doi.org/10.1007/BF01261989

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  • DOI: https://doi.org/10.1007/BF01261989

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