Conditioning of semidefinite programs

This paper studies the conditioning of semidefinite programs by analyzing t he effect of small perturbations in problem data on the solution. Under the assumptions of strict complementarity and nondegeneracy, an explicit bound on the change in the solution is derived in a primal-dual framework, using tools from the Kantorovic theory. This approach also quantifies the size o f permissible perturbations. We include a discussion of these results for b lock diagonal semidefinite programs, of which linear programming is a speci al case.