The subject of real-time, steady-state optimization under significant uncertainty is addressed in this paper. Specifically, the use of constraint-adaptation schemes is reviewed, and it is shown that, in general, such schemes cannot guarantee process feasibility over the relevant input space during the iterative process. This issue is addressed via the design of a feasibility-guaranteeing input filter, which is easily derived through the use of a Lipschitz bound on the plant behavior.While the proposed approach works to guarantee feasibility for the single-constraint case, early sub-optimal convergence is noted for cases with multiple constraints. In this latter scenario, some constraint violations must be accepted if convergence to the optimum is desired. An illustrative example is given to demonstrate these points.