East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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AN ELIGIBLE PRIMAL-DUAL INTERIOR-POINT METHOD FOR LINEAR OPTIMIZATION

  • Cho, Gyeong-Mi (Department of Software Engineering, Dongseo University) ;
  • Lee, Yong-Hoon (Department of Mathematics, Pusan National University)
  • Received : 2013.03.26
  • Accepted : 2013.04.18
  • Published : 2013.06.01
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Abstract

It is well known that each kernel function defines a primal-dual interior-point method(IPM). Most of polynomial-time interior-point algorithms for linear optimization(LO) are based on the logarithmic kernel function([2, 11]). In this paper we define a new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has ${\mathcal{O}}((log\;p){\sqrt{n}}\;log\;n\;log\;{\frac{n}{\epsilon}})$ and ${\mathcal{O}}((q\;log\;p)^{\frac{3}{2}}{\sqrt{n}}\;log\;{\frac{n}{\epsilon}})$ iteration bound for large- and small-update methods, respectively. These are currently the best known complexity results.

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References

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