This paper investigates convergence and optimality properties of the modified two-step algorithm for on-line determination of the optimum steady-state operating point of an industrial process. Mild sufficient conditions are derived for the convergence and feasibility of the algorithm. It is shown that every point within the solution set of the algorithm satisfies first-order necessary conditions for optimality, and that every optimal solution belongs to this set. It is also shown that there are advantages to be gained by using a linear mathematical model of the process within the implementation of the algorithm.