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A Polynomial-time Interior-point Algorithm for Convex QuadraticSemidefinite Optimization

Published online by Cambridge University Press:  25 October 2010

Y. Q. Bai ,
F. Y. Wang  and
X. W. Luo
Y. Q. Bai
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China. yqbai@shu.edu.cn
F. Y. Wang
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China. yqbai@shu.edu.cn
X. W. Luo
Affiliation:
Department of Mathematics, Shanghai University, Shanghai, 200444, P.R. China. yqbai@shu.edu.cn
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Abstract

In this paper we propose a primal-dual interior-point algorithm forconvex quadratic semidefinite optimization problem. The searchdirection of algorithm is defined in terms of a matrix function andthe iteration is generated by full-Newton step. Furthermore, wederive the iteration bound for the algorithm with small-updatemethod, namely, O( $\sqrt{n}$ log $\frac{n}{\varepsilon}$ ), which isbest-known bound so far.

Keywords

Convex quadratic semidefinite optimizationinterior-pointalgorithmsmall-update methoditeration boundpolynomial-time

Information

Type
Research Article
Information
RAIRO - Operations Research , Volume 44 , Issue 3 , July 2010 , pp. 251 - 265
Copyright
© EDP Sciences, ROADEF, SMAI, 2010

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