The ability of a model-based real-time optimization (RTO) scheme to converge to the plant optinium relies on the ability of the underlying process model to predict the plant's necessary conditions of optirtiality (NCO). These include the values and gradients of the active constraints, as well as the gradient of the cost function. Hence, in the presence of plant-model mismatch or unmeasured disturbances, one could use (estimates of) the plant NCO to track the plant optimum, This paper shows how to formulate a modifed optimization problem that incorporates such information. The so-called modifiers, which express the difference between the measured or estimated plant NCO and those predicted by the model, are added to the constraints and the cost function of the modified optimization problem and are adapted iteratively. Local convergence and model-adequacy issues are analyzed. The modifier-adaptation scheme is tested experimentally via the RTO of it three-tank system.