Primal-dual interior-point algorithms for second-order cone optimization based on kernel functions

被引：40

作者：

Bai, Y. Q. ^{[1
]}

Wang, G. Q.

Roos, C. ^{[2
]}

机构：

[1] Shanghai Univ, Dept Math, Coll Sci, Shanghai 200444, Peoples R China

[2] Delft Univ Technol, Fac Elect Engn Math & Comp Sci, NL-2600 GA Delft, Netherlands

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 70卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Second-order cone optimization; Interior-point methods; Primal-dual method; Large- and small-update methods; Polynomial complexity; LINEAR OPTIMIZATION; SYMMETRIC CONES; JORDAN ALGEBRAS; SEMIDEFINITE; CONVERGENCE; DIRECTIONS;

D O I：

10.1016/j.na.2008.07.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present primal-dual interior-point algorithms for second-order cone optimization based on a wide variety of kernel functions. This class of kernel functions has been investigated earlier for the case of linear optimization. In this paper we derive the iteration bounds O(root N log N) log N/epsilon for large- and O(root N) log N/epsilon for small-update methods, respectively. Here N denotes the number of second-order cones in the problem formulation and epsilon the desired accuracy. These iteration bounds are currently the best known bounds for Such methods. Numerical results show that the algorithms are efficient. (C) 2008 Elsevier Ltd. All rights reserved.

引用

页码：3584 / 3602

页数：19

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