In the framework of process optimization, measurements can be used to compensate for the effect of uncertainty. The method studied in this paper combines a process model and measurements to iteratively improve the operation of continuous processes. Unlike many existing real-time optimization schemes, the measurements are not used to update the process model, but to adapt the constraints in the optimization problem. Upon convergence, all the constraints are respected even in the presence of large model mismatch. Moreover, it is shown that constraints adaptation can handle changes in the set of active constraints. The approach is illustrated, via numerical simulation, for the optimization of a continuous stirred-tank reactor.