in this talk, i will talk about the parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function along a fixed direction and on a compact set. for the perturbation along a fixed direction, it is proven that the continuity of the optimal set mapping could fail on a nonlinearity interval and the set of points where this failure occurs is finite. a numerical method is developed to numerically compute the nonlinearity interval and generalize to perturbations on a compact set. for multi-variable perturbations, a maximal analytic perturbation set (maps) is defined on which the analyticity of the optimal mapping holds. numerical examples are given to demonstrate the performance.