Geodesic
Limiting behavior and analyticity of two special types of infeasible weighted central paths in semidefinite programming
Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 1 
M. Trnovská. Limiting behavior and analyticity of two special types of infeasible
weighted central paths in semidefinite programming. Acta mathematica Universitatis Comenianae, Tome 79 (2010) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2010_79_1_a12/
@article{AMUC_2010_79_1_a12,
     author = {M. Trnovsk\'a},
     title = {Limiting behavior and analyticity of two special types of infeasible
weighted central paths in semidefinite programming},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2010},
     volume = {79},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2010_79_1_a12/}
}
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The central path is the most important concept in the theory of interior point methods. It is an analytic curve in the interior of the feasible set which tends to an optimal point at the boundary. The analyticity properties of the paths are connected to the analysis of the superlinear convergence of the interior point algorithms for semidefinite programming. In this paper we study the analyticity of two special types of weighted central paths in semidefinite programming, under the condition of the existence of the strictly complementary solution.