An input/output model reduction-based optimization scheme for large-scale systems

A reduced model based optimization strategy is presented for the cases where input/output codes are the process simulators of choice, and thus system Jacobians and even system equations are not explicitly available to the user. The former is the case when commercial software packages or legacy codes are used to simulate a large-scale system and the latter when microscopic or multiscale simulators are employed. When such black-box dynamic simulators axe used, we perform optimization by combining the recursive projection method [G. M. Shroff and H. B. Keller, SIAM J. Numer. Anal., 30 (1993), pp. 1099-1120] which identifies the (typically) low-dimensional slow dynamics of the (dissipative) model with a second reduction to the low-dimensional subspace of the decision variables. This results in the solution of a low-order unconstrained optimization problem. Optimal conditions are then computed in an efficient way using only low-dimensional numerical approximations of gradients and Hessians. The tubular reactor is used as an illustrative example to demonstrate this model reduction-based optimization methodology. © 2005 Society for Industrial and Applied Mathematics.