In this paper, we present an inexact sequential quadratic programming method in the context of a direct multiple shooting approach for differential algebraic equations. For the case that a numerical integration routine is used to compute the states of a relaxed differential algebraic equation, the computation of sensitivities, with respect to a large number of algebraic states, can become very expensive. To overcome this limitation, the inexact sequential quadratic programming method that we propose in this paper requires neither the computation of any sensitivity direction of the differential state trajectory, with respect to the algebraic states, nor the consistent initialization of the differential algebraic equation. We prove the locally quadratic convergence of the proposed method. Finally, we demonstrate the numerical performance of the method by optimizing a distillation column with 82 differential and 122 algebraic states. Copyright © 2012 John Wiley & Sons, Ltd.