Journal of the Korean Society for Industrial and Applied Mathematics

  • 제14권2호
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  • Pages.93-111
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  • 2010
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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ON COMPLEXITY ANALYSIS OF THE PRIMAL-DUAL INTERIOR-POINT METHOD FOR SECOND-ORDER CONE OPTIMIZATION PROBLEM

  • Choi, Bo-Kyung (DEPARTMENT OF APPLIED MATHEMATICS, PUKYONG NATIONAL UNIVERSITY) ;
  • Lee, Gue-Myung (DEPARTMENT OF APPLIED MATHEMATICS, PUKYONG NATIONAL UNIVERSITY)
  • 투고 : 2010.05.26
  • 심사 : 2010.06.02
  • 발행 : 2010.06.25
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초록

The purpose of this paper is to obtain new complexity results for a second-order cone optimization (SOCO) problem. We define a proximity function for the SOCO by a kernel function. Furthermore we formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOCO by using the proximity function and give its complexity analysis, and then we show that the new worst-case iteration bound for the IPM is $O(q\sqrt{N}(logN)^{\frac{q+1}{q}}log{\frac{N}{\epsilon})$, where $q{\geqq}1$.

키워드

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