Journal of Optimization Theory and Applications

, Volume 138, Issue 3, pp 341–359 | Cite as

A Class of Large-Update and Small-Update Primal-Dual Interior-Point Algorithms for Linear Optimization

  • Y. Q. Bai
  • G. Lesaja
  • C. Roos
  • G. Q. Wang
  • M. El Ghami


In this paper we present a class of polynomial primal-dual interior-point algorithms for linear optimization based on a new class of kernel functions. This class is fairly general and includes the classical logarithmic function, the prototype self-regular function, and non-self-regular kernel functions as special cases. The analysis of the algorithms in the paper follows the same line of arguments as in Bai et al. (SIAM J. Optim. 15:101–128, [2004]), where a variety of non-self-regular kernel functions were considered including the ones with linear and quadratic growth terms. However, the important case when the growth term is between linear and quadratic was not considered. The goal of this paper is to introduce such class of kernel functions and to show that the interior-point methods based on these functions have favorable complexity results. They match the currently best known iteration bounds for the prototype self-regular function with quadratic growth term, the simple non-self-regular function with linear growth term, and the classical logarithmic kernel function. In order to achieve these complexity results, several new arguments had to be used.


Linear optimization Interior-point methods Primal-dual methods Complexity Kernel functions 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Y. Q. Bai
    • 1
  • G. Lesaja
    • 2
  • C. Roos
    • 3
  • G. Q. Wang
    • 1
  • M. El Ghami
    • 4
  1. 1.Department of MathematicsShanghai UniversityShanghaiChina
  2. 2.Department of Mathematical SciencesGeorgia Southern UniversityStatesboroUSA
  3. 3.Faculty of Electrical Engineering, Mathematics, and Computer ScienceDelft University of TechnologyDelftNetherlands
  4. 4.Department of Computer ScienceUniversity of BergenBergenNorway

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