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On the central path for nonlinear semidefinite programming

Published online by Cambridge University Press:  15 August 2002

L. M. Grana Drummond ,
Alfredo Noel Iusem  and
B. F. Svaiter
L. M. Grana Drummond
Affiliation:
Programa de Engenharia de Sistemas de Computação, COPPE-UFRJ, CP 68511, Rio de Janeiro - RJ 21945-970, Brazil.
Alfredo Noel Iusem
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro-RJ 22460-320, Brazil.
B. F. Svaiter
Affiliation:
Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro-RJ 22460-320, Brazil.
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Abstract

In this paper we study the well definedness of the central path associated to agiven nonlinear (convex) semidefinite programming problem. Under standard assumptions,we establish that the existence of the central path is equivalent to the nonemptiness andboundedness of the optimal set. Other equivalent conditions are given, such as the existenceof a strictly dual feasible point or the existence of a single central point.The monotonicbehavior of the logarithmic barrier and the objective function along the trajectory is alsodiscussed. Finally, the existence and optimality of cluster points are established.

Keywords

Nonlinear semidefinite programmingsemidefinite programmingcentral pathlogarithmic barrier functionconvex programming.
Type
Research Article
Information
RAIRO - Operations Research , Volume 34 , Issue 3 , July 2000 , pp. 331 - 345
Copyright
© EDP Sciences, 2000

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