Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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NEW COMPLEXITY ANALYSIS OF PRIMAL-DUAL IMPS FOR P* LAPS BASED ON LARGE UPDATES

  • Cho, Gyeong-Mi (DEPARTMENT OF MULTIMEDIA ENGINEERING DONGSEO UNIVERSITY) ;
  • Kim, Min-Kyung (DEPARTMENT OF MATHEMATICS PUSAN NATIONAL UNIVERSITY)
  • Published : 2009.05.31
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Abstract

In this paper we present new large-update primal-dual interior point algorithms for $P_*$ linear complementarity problems(LAPS) based on a class of kernel functions, ${\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{1}{\sigma}}(e^{{\sigma}(1-t)}-1)$, p $\in$ [0, 1], ${\sigma}{\geq}1$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*$ LAPS have $O((1+2+\kappa)n^{{\frac{1}{p+1}}}lognlog{\frac{n}{\varepsilon}})$ complexity bound. When p = 1, we have $O((1+2\kappa)\sqrt{n}lognlog\frac{n}{\varepsilon})$ complexity which is so far the best known complexity for large-update methods.

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References

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