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nonlinear semidefinite programming

RAIRO - Operations Research (1)

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On the central path for nonlinear semidefinite programming
L. M. Grana Drummond, Alfredo Noel Iusem, B. F. Svaiter
Journal:

RAIRO - Operations Research / Volume 34 / Issue 3 / July 2000

Published online by Cambridge University Press:

15 August 2002, pp. 331-345

Print publication:

July 2000
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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.