On approximate solutions for robust convex semidefinite optimization problems

In this paper, we consider approximate solutions (ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-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 ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\epsilon $$\end{document}-solutions in robust convex semidefinite programming problem under the robust characteristic cone constraint qualification. Moreover, an example is given to illustrate the obtained results.