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In the batch process industry, the available models carry a large amount of uncertainty and can seldom be used to directly optimize real processes. Several measurement-based optimization methods have been proposed to deal with model mismatch and process disturbances. Constraints often play a dominant role in the dynamic optimization of batch processes. In their presence, the optimal input profiles are characterized by a set of arcs, switching times and active path and terminal constraints. This paper presents a novel method tailored to those problems where the potential of optimization arises mainly from the correct set of path and terminal constraints being active. The input profiles are computed between successive runs by dynamic optimization of a fixed nominal model, and the constraints in the optimization problem are adapted using measured information from previous batches. Note that, unlike many existing optimization schemes, the measurements are not used to update the process model. Moreover, the proposed approach has the potential to uncover the optimal input structure. This is demonstrated on a simple semi-batch reactor example.