We consider the constantly scaled H infinity, control problem related to the robust performance against structured time-varying uncertainties. The problem is not convex in general for the output feedback synthesis, and hence it is difficult to find a global solution. The purpose of this work is to provide two algorithms named W-L and W-Y iterations for local optimization based on linear matrix inequality (LMI) conditions. We show that the W-L iteration is superior to the well-known D-K iteration in the sense that fewer parameters are fixed in the W-L iteration than the D-K iteration, i.e. the searching area in the W-L iteration is much bigger than that in the D-K iteration. We also show that the W-K iteration is slightly better than the D-K iteration in the sense that the space of variable parameters in the W-Y iteration is larger than that for the D-K iteration. We confirm the above properties by two types of numerical examples.