Limiting behaviour and analyticity of weighted central paths in semidefinite programming

Margaréta Halická, Mária Trnovská
2010 Optimization Methods and Software  
In this paper we analyze the limiting behavior of infeasible weighted central paths in semide nite programming under the assumption that a strictly complementary solution exists. We show that the paths associated with the \square root"symmetrization of the weighted centrality condition are analytic functions of the barrier parameter even at = 0 if and only if the weight matrix is block diagonal in terms of optimal block partition of variables. This result strengthens some recent result by Lu
more » ... ent result by Lu and Monteiro establishing the analyticity of the paths as functions of p at = 0. Moreover, in this paper we study the analytical properties of the paths associated with the \Cholesky factor"symmetrization. We show that the paths exhibit the same analytical behavior at = 0 as the paths corresponding to the square root symmetrization.
doi:10.1080/10556780903239493 fatcat:vocgvgr44rh5hozo2h3bddcave