Computable error bounds for semidefinite programming

We study computability and applicability of error bounds for a given semide finite pro-gramming problem under the assumption that the recession functio n associated with the constraint system satisfies the Slater condition. Spe cifically, we give computable error bounds for the distances between feasib le sets, optimal objective values, and optimal solution sets in terms of an upper bound for the condition number of a constraint system, a Lipschitz c onstant of the objective function, and the size of perturbation. Moreover, we are able to obtain an exact penalty function for semidefinite programmin g along with a lower bound for penalty parameters. We also apply the result s to a class of statistical problems.