East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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COMPLEXITY ANALYSIS OF IPM FOR $P_*(\kappa)$ LCPS BASED ON ELIGIBLE KERNEL FUNCTIONS

  • Kim, Min-Kyung (Department of Mathematics Pusan National University) ;
  • Cho, Gyeong-Mi (Department of Multimedia Engineering Dongseo University)
  • Received : 2008.06.30
  • Accepted : 2008.11.29
  • Published : 2009.03.31
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Abstract

In this paper we propose new large-update primal-dual inte-rior point algorithms for $P_*(\kappa)$ linear complementarity problems(LCPs). New search directions and proximity measures are proposed based on the kernel function$\psi(t)=\frac{t^{p+1}-1}{p+1}+\frac{e^{\frac{1}{t}}-e}{e}$,$p{\in}$[0,1]. We showed that if a strictly feasible starting point is available, then the algorithm has $O((1+2\kappa)(logn)^{2}n^{\frac{1}{p+1}}log\frac{n}{\varepsilon}$ complexity bound.

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References

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