  


Limiting behavior of the AlizadehHaeberlyOverton weighted paths in semidefinite programming
Zhaosong Lu (zhaosongisye.gatech.edu) Abstract: This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming obtained from centrality equations of the form $X S + SX = 2 \nu W$, where $W$ is a fixed positive definite matrix and $\nu>0$ is a parameter, under the assumption that the problem has a strictly complementary primaldual optimal solution. It is shown that a weighted central path as a function of $\nu$ can be extended analytically beyond $0$ and hence that the path and its derivatives converge as $\nu \downarrow 0$. Characterization of the limit points and firstorder derivatives of the scaled weighted central path is also provided. We finally derive an error bound on the distance between a point lying in a certain neighborhood of the central path and the set of primaldual optimal solutions. Keywords: limiting behavior, weighted central path, error bound,semidefinite programming. Category 1: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Manuscript, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, July 2003. Download: [Postscript][PDF] Entry Submitted: 07/23/2003 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  