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, Volume 12, Issue 2, pp 209–275 | Cite as

On self-regular IPMs

  • Maziar Salahi
  • Renata Sotirov
  • Tamás Terlaky
Article

Abstract

Primal-dual interior-point methods (IPMs) have shown their power in solving large classes of optimization problems. However, at present there is still a gap between the practical behavior of these algorithms and their theoretical worst-case complexity results, with respect to the strategies of updating the duality gap parameter in the algorithm. The so-called small-update IPMs enjoy the best known theoretical worst-case iteration bound, but work very poorly in practice. To the contrary, the so-called large-update IPMs have superior practical performance but with relatively weaker theoretical results. In this paper we discuss the new algorithmic variants and improved complexity results with respect to the new family of Self-Regular proximity based IPMs for Linear Optimization problems, and their generalizations to Conic and Semidefinite Optimization

Key Words

Linear optimization semidefinite optimization conic optimization primal-dual interior-point method self-regular proximity function polynomial complexity 

AMS subject classification

90C05 90C22 90C51 

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Copyright information

© Sociedad de Estadística e Investigación Operativa 2004

Authors and Affiliations

  • Maziar Salahi
    • 1
  • Renata Sotirov
    • 2
  • Tamás Terlaky
    • 2
  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  2. 2.Advanced Optimization Laboratory, Department of Computing & SoftwareMcMaster UniversityHamiltonCanada

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