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This paper describes a fast algorithm for the prioritized kinematic control of redundant manipulators. Building on the classical prioritized task framework, the focus is set on efficient computation and handling of inequality constraints throughout priority levels. Classical approaches that tend to account for inequality constraints through potential fields are computationally competitive but have quality issues. Formulating the same control problems with a Quadratic Program (QP) removes these issues but is known to be costly. The following work revisits the formulation of a hierarchy of QPs for the prioritized control of redundant manipulators and proposes an algorithm that can meet real time requirements for current humanoid robots. Because lower control objectives often become infeasible, a particular point of focus is the numerical stability, hereby addressed with Tikhonov regularization. The method was tested in simulation for the control of the humanoid robot HRP-2.