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PREDICTOR–CORRECTOR SMOOTHING NEWTON METHOD FOR SOLVING SEMIDEFINITE PROGRAMMING

Published online by Cambridge University Press:  17 April 2009

CAIYING WU  and
GUOQING CHEN
CAIYING WU*
Affiliation:
College of Mathematics Science, Inner Mongolia University, Hohhot 010021, People’s Republic of China (email: wucaiyingun@163.com)
GUOQING CHEN
Affiliation:
College of Mathematics Science, Inner Mongolia University, Hohhot 010021, People’s Republic of China (email: cgq@imu.edu.cn)
*
✉For correspondence; e-mail: wucaiyingun@163.com
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Abstract

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There has been much interest recently in smoothing methods for solving semidefinite programming (SDP). In this paper, based on the equivalent transformation for the optimality conditions of SDP, we present a predictor–corrector smoothing Newton algorithm for SDP. Issues such as the existence of Newton directions, boundedness of iterates, global convergence, and local superlinear convergence of our algorithm are studied under suitable assumptions.

Keywords

semidefinite complementaritysemidefinite programmingFischer–Burmeister functionsuperlinear convergence

MSC classification

Secondary: 90C22: Semidefinite programming
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 367 - 376
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

Project supported by the Teaching and Research Award Program for the Outstanding Young Teachers in Higher Education Institutes of Ministry of Education, People’s Republic of China.

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