In order to deal with plant-model mismatch, iterative process optimization schemes use some adaptation strategy based on measurements. The modifier-adaptation approach consists in performing first-order corrections of the cost and constraint functions in the model-based optimization problem. The approach has the ability to converge to the true process optimum but the first-order corrections require the experimental estimation of the process gradients. Dual modifier-adaptation algorithms estimate the gradients by finite difference approximation based on the measurements obtained at the current and past operating points. In order to guarantee the accuracy of the estimated gradients a constraint is added to the optimization problem in order to position the next operating points with respect to the previous ones. This paper presents an alternative first-order correction, which provides an improved approximation of the cost and constraint functions, together with a new gradient error constraint for use in dual modifier adaptation. By means of the Williams-Otto reactor case study, the new dual modifier-adaptation approach is compared in simulation with a previous approach found in the literature showing faster convergence to a neighborhood of the plant optimum. (C) 2013 Elsevier Ltd. All rights reserved.