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A new barrier for a class of semidefinite problems

Published online by Cambridge University Press:  08 November 2006

Erik A. Papa Quiroz  and
Paolo Roberto Oliveira
Erik A. Papa Quiroz
Affiliation:
Programa de Engenharia de Sistemas e Computacão, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; erik@cos.ufrj.br
Paolo Roberto Oliveira
Affiliation:
Programa de Engenharia de Sistemas e Computacão, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; erik@cos.ufrj.br Rua Honorio, 1144 c 5, 20771-421, Rio de Janeiro, Brazil; poliveir@cos.ufrj.br
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Abstract

We introduce a new barrier function to solve a class of Semidefinite Optimization Problems (SOP) with bounded variables. That class is motivated by some (SOP) as the minimization of the sum of the first few eigenvalues of symmetric matrices and graph partitioning problems. We study the primal-dual central path defined by the new barrier and we show that this path is analytic, bounded and that all cluster points are optimal solutions of the primal-dual pair of problems. Then, using some ideas from semi-analytic geometry we prove its full convergence. Finally, we introduce a new proximal point algorithm for that class of problems and prove its convergence.

Keywords

Interior point methodsbarrier functioncentral pathsemidefinite optimization.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 3 , July 2006 , pp. 303 - 323
Copyright
© EDP Sciences, 2006

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References

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