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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 for convex quadratic semidefinite optimization problem. The search direction of algorithm is defined in terms of a matrix function and the iteration is generated by full-Newton step. Furthermore, we derive the iteration bound for the algorithm with small-update method, namely, O($\sqrt{n}$ log $\frac{n}{\varepsilon}$), which is best-known bound so far.

Keywords

Convex quadratic semidefinite optimizationinterior-point algorithmsmall-update methoditeration boundpolynomial-time
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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