Conditioning of semidefinite programs

This paper studies the conditioning of semidefinite programs by analyzing the effect of small perturbations in problem data on the solution. Under the assumptions of strict complementarity and non-degeneracy, an explicit bound on the change in the solution is derived in a primal–dual framework, using tools from the Kantorovič theory. This approach also quantifies the size of permissible perturbations. We include a discussion of these results for block diagonal semidefinite programs, of which linear programming is a special case.