- Limiting behavior of the Alizadeh-Haeberly-Overton weighted paths in semidefinite programming Zhaosong Lu (zhaosongisye.gatech.edu) Renato D. C. Monteiro (monteiroisye.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 primal-dual 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 first-order 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 primal-dual optimal solutions. Keywords: limiting behavior, weighted central path, error bound,semidefinite programming. Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Citation: Manuscript, School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA 30332, July 2003. Download: [Postscript][PDF]Entry Submitted: 07/23/2003Entry Accepted: 07/23/2003Entry Last Modified: 12/12/2004Modify/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 Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.