Split and bound method for process optimization under parametric uncertainty

We discuss methods for solving steady state process optimization problems under parametric uncertainty. The problem is formulated as a two-stage optimization problem (TSOP) which is inherently multiextremal and nondifferentiable. An indirect approach (split and bound method, SB) has been developed to address the nondifferentiability issue. The SB method iteratively solves for lower and upper bounds of the TSOP objective function, such that in the limit these bounds sandwich the optimal solution to within a given tolerance, thus avoiding the explicit solution of the nondifferentiable TSOP. We have introduced a linearization approach, which can lead to significant computational savings. Heuristics are proposed for partitioning and selection of critical points for the lower bound problem. We illustrate the proposed approach with one computational experiment