On approximate solutions for robust convex semidefinite optimization problems

In this paper, we consider approximate solutions ((epsilon )-solutions) for a convex semidefinite programming problem in the face of data uncertainty. Using robust optimization approach (worst-case approach), we prove an approximate optimality theorem and approximate duality theorems for (epsilon )-solutions in robust convex semidefinite programming problem under the robust characteristic cone constraint qualification. Moreover, an example is given to illustrate the obtained results.