Inaccurate models limit the performance of model-based real-time optimization (RTO) and even cause system instability. Therefore, a RTO framework that can guarantee global convergence with the presence of plant-model mismatch is desired. In this regard, the trust-region framework is simple to implement and guarantees globally convergent for unconstrained problems. However, it remains to be seen if the trust-region strategy can handle inequality constraints directly with the common model adaptation method. This paper addresses this issue and proposes a novel composite-step trust-region framework that guarantees global convergence for constrained RTO problems. The trial step is decomposed into a normal step that improves feasibility and a tangential step that reduces the cost function. In each iteration, the model optimization problem with relaxed constraints is solved. The proof of the global convergence property under structural plant-model mismatch is given.

The generalized pooling problem (GPP) is a NP-hard problem for which the solution time for securing a global optimal solution heavily depends on the strength of the problem formulation. The existing GPP formulations use either quality variables (P-formulation and the variants) or split-fraction variables (SF-formulation and the variants) to model the material balance at the pools. This paper is the first attempt to develop theoretical results for comparing the strength of P-formulation and SF-formulation. It is found that, an enhanced version of P-formulation, called P+-formulation, is at least as strong as SF-formulation under mild conditions. Furthermore, P+-formulation becomes identical to P-formulation when the pooling network comprises only mixers and splitters. With additional conditions that are often satisfied at the root node, P-formulation is proved to be as least as strong as SF-formulation. The theoretical results are verified by the computational study of 23 problem instances.