In the context of real-time optimization, modifier-adaptation schemes update the model-based optimization problem by adding first-order correction terms to the cost and constraint functions of the optimization problem. This guarantees meeting the plant first-order optimality conditions upon convergence, despite the presence of parametric and structural plant-model mismatch. An alternative modifier-adaptation strategy has been proposed, wherein the first-order corrections are applied to the output functions rather than to the cost and constraint functions. This paper analyzes this alternative adaptation scheme in detail and provides arguments for its use in cases where the cost and constraints are nonlinear functions of the inputs and outputs. The approach is illustrated in simulation on the Williams-Otto continuous stirred-tank reactor. (C) 2018 Elsevier Ltd. All rights reserved.