Real-time optimization (RTO) is not always able to achieve optimal process operation due to the presence of significant uncertainty in the plant models that are used to make decisions. Modifier adaptation (MA) overcomes these issues by modifying the cost and constraint functions of the economic optimization problem solved at the RTO level to drive the process to optimality. This paper proposes an alternative MA methodology for dealing with process-dependent constraints without increasing the number of modifiers. The key feature consists in computing the modifiers from the gradient of the Lagrangian function, thereby requiring a single gradient modifier per process input. The approach is illustrated in simulation via the nested modifier-adaptation (NMA) scheme implemented on a depropanizer distillation column that is characterized by a significant amount of uncertainty. The convergence of the proposed Lagrangian-based NMA scheme is significantly faster than that of standard NMA. (C) 2018 Published by Elsevier Ltd.