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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
Programa de Engenharia de Sistemas e Computacão, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil;
Paolo Roberto Oliveira
Programa de Engenharia de Sistemas e Computacão, COPPE, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil; Rua Honorio, 1144 c 5, 20771-421, Rio de Janeiro, Brazil;
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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.

Research Article
© EDP Sciences, 2006

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