This paper deals with the real-time optimization of uncertain plants and proposes an approach based on surrogate models to reach the plant optimum when the plant cost gradient is imperfectly known. It is shown that, for processes with only box constraints, the optimum is reached upon convergence if the multiplicative gradient uncertainty lies within some bounded interval. For the case of general constraints, conditions are derived that guarantee plant feasibility and, in principle, allow enforcing cost decrease at each iteration.