Enables minimization of steady-state objective function P(z∞), subject to a set of constraints zmin≦z∞≦zmax, and under the assumption that the values of the state vector, z, at different points in time related via a model expressed in dynamic open equation format Q(z∞, zk, zk-1, zk-2, . . . , zk-n)=0, where z∞ is predicted final value of state vector, z, and zk, zk-1, zk-2, . . . , zk-n are current and previous values of state vector, z. Determines optimum operation of an industrial process having steady-state objective function P(z∞), including: receiving outputs from the process; minimizing steady-state objective function P(z∞) subject to set of constraints zmin≦z∞≦zmax; wherein values of state vector at different times are related via model of form Q(z∞, zk, zk-1, zk-2, . . . , zk-n)=0; to minimize objective function P(z∞). Industrial process to be optimised may include measured and unmeasured process variables.