# 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)
• Accepted : 2010.06.02
• Published : 2010.06.25

#### 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 $q{\geqq}1$.

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