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http://dx.doi.org/10.12941/jksiam.2010.14.2.093

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)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.14, no.2, 2010 , pp. 93-111 More about this Journal
Abstract
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 $q{\geqq}1$.
Keywords
second-order cone optimization problem; primal-dual interior-point methods; kernel function; proximity function; complexity analysis; worst-case iteration bound;
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