In the context of real-time optimization, modifier-adaptation schemes use estimates of the plant gradients to achieve plant optimality despite plant-model mismatch. Plant feasibility is guaranteed upon convergence, but not at the successive operating points computed by the algorithm prior to convergence. This paper presents a strategy for guaranteeing rigorous constraint satisfaction of all iterates in the presence of plant-model mismatch and uncertainty in the gradient estimates. The proposed strategy relies on constructing constraint upper-bounding functions that are robust to the gradient uncertainty that results when the gradients are estimated by finite differences from noisy measurements. The performance of the approach is illustrated for the optimization of a continuous stirred-tank reactor. (C) 2016 Elsevier Ltd. All rights reserved.