In this paper we consider infinite dimensional optimization problems with equality constraints. The basic underlying algorithm is a reduced SQP method. We give a global convergence proof in Hilbert space and extend this analysis to inexact reduced SQP methods. These methods are useful when discretizing the infinite dimensional problems and solving the resulting large scale discretized optimization problems. The convergence analysis takes into account the Maratos effect which occurs for nonsmooth norms. The inexact reduced SQP method is applied to a discretized parabolic control problem