In this paper, we propose a new approach to the optimal control problem for linear time invariant systems subject to input constraints. The input constraint is described by means of integral quadratic constraints in order to obtain an accurate model for the nonlinearity. The key point of this work is to use the IQC information on the design stage to improve the closed-loop performance. We apply this strategy to the input saturation problem by using a combination of multipliers and propose an algorithm to tune some parameters associated with the IQC. Numerical examples show that this strategy can significantly improve the performance of the system when compared with the circle and Popov criteria.