Abstract: We considered a class of sum of squares convex polynomial optimization problems with uncertain parameters. Firstly, we proposed a robust counterpart optimization model for the uncertain sum of squares convex polynomial optimization problem with the help of robust optimization method. Secondly, by using a class of robust type characteristic cone constraint qualifications, we established exact SDP relaxation problem for this optimization problem. Finally, we introduced a Lagrangian function of this uncertain sum of squares convex polynomial optimization problem, and gave robust saddle point theorems of this uncertain sum of squares convex polynomial optimization problem with the help of sum of squares conditions.

Key words: sum of squares convex polynomial optimization, saddle point, sum of squares condition, SDP relaxation problem