The conventional way of solving this type of optimization problems is to transform them into Semi-Definite Programs (SDPs) which are then solved using interior-point algorithms. The disadvantage of this approach is that the transformation introduces additional decision variables. In many situations, these auxiliary decision variables become the main computational burden, and the conventional method then becomes very inefficient and time consuming. In this talk, a number of specialized algorithms for solving optimization problems arising from IQC analysis are presented. The crucial advantage of these newly developed algorithms is that no auxiliary decision variables are introduced. The results of our numerical experiments confirm that these algorithms can solve a problem arising from IQC analysis much faster than the conventional approach does.