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Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function

Authors:	Yan Qin Bai Guo Qiang Wang

Institution:	(1) Department of Mathematics, College of Sciences, Shanghai University, Shanghai, 200444, P. R. China;(2) College of Vocational Technology, Shanghai University of Engineering Science, Shanghai, 200437, P. R. China

Abstract:	A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function, with parameters p and q, is presented. Its growth term is between linear and quadratic. Some new tools for the analysis of the algorithms are proposed. The complexity bounds of $O{\left( {{\sqrt N }\log N\log \frac{N} {\varepsilon }} \right)}$ for large-update methods and $O{\left( {{\sqrt N }\log \frac{N} {\varepsilon }} \right)}$ for small-update methods match the best known complexity bounds obtained for these methods. Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q. Project sponsored by Shanghai Pujiang Program (Grant No. 06PJ14039) and Shanghai Educational Committee Foundation (Grant No. 06NS031)

Keywords:	second-order cone optimization linear optimization interior-point methods large- and small-update methods polynomial-time complexity
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