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Properties of the Central Path

  • Hans Frenk
  • Kees Roos
  • Tamás Terlaky
  • Shuzhong Zhang
Part of the Applied Optimization book series (APOP, volume 33)

Abstract

In this chapter, we take a careful look at the behavior of the central path, when it approaches the optimal solution set of a semidefinite program. We will demonstrate that the primal-dual central path converges to the analytic center of the optimal solution set. Moreover, the distance to this analytic center from any point on the central path is shown to converge at the same R-rate as the duality gap. This result can be interpreted as an error-bound for solutions on the central path, with respect to the optimal solution set. Underlying the analysis is an assumption that a strictly complementary solution pair for the semidefinite program exists.

Keywords

Analytic Center Central Path Semidefinite Program Strict Complementarity Dual Optimal Solution 
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.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Hans Frenk
    • 1
  • Kees Roos
    • 2
  • Tamás Terlaky
    • 2
  • Shuzhong Zhang
    • 1
  1. 1.Erasmus UniversityRotterdamThe Netherlands
  2. 2.Delft University of TechnologyThe Netherlands

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