Volume 34, Number 3, July September 2000
|Page(s)||331 - 345|
|Published online||15 August 2002|
On the central path for nonlinear semidefinite programming
Programa de Engenharia de Sistemas de
Computação, COPPE-UFRJ, CP 68511, Rio de Janeiro - RJ
2 Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Jardim Botânico, Rio de Janeiro-RJ 22460-320, Brazil.
In this paper we study the well definedness of the central path associated to a given nonlinear (convex) semidefinite programming problem. Under standard assumptions, we establish that the existence of the central path is equivalent to the nonemptiness and boundedness of the optimal set. Other equivalent conditions are given, such as the existence of a strictly dual feasible point or the existence of a single central point.The monotonic behavior of the logarithmic barrier and the objective function along the trajectory is also discussed. Finally, the existence and optimality of cluster points are established.
Key words: Nonlinear semidefinite programming / semidefinite programming / central path / logarithmic barrier function / convex programming.
© EDP Sciences, 2000
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.