Limiting behaviour and analyticity of weighted central paths in semidefinite programming
This paper studies limiting behaviour of infeasible weighted central paths in semidefinite programming under strict complementarity assumption. It is known that weighted central paths associated with the 'Cholesky factor' symmetrization of the -parameterized centring condition are well defined for some classes of weight matrices, and they are analytic functions of for 0, sufficiently small. In this paper, we show that these paths, considered as functions of root, can be analytically extended to =0. Moreover, we show that the paths are analytic functions of at =0 if and only if the weight matrix is block diagonal in terms of the optimal block partition of variables.
analyticity weighted central path semidefinite programming interior-point methods