Acceleration of reduced Hessian methods for large-scale nonlinear programming

Abstract Process optimization problems are frequently characterized by large models, with many variables and constraints but relatively few degrees of freedom. Reduced Hessian decomposition methods applied to successive quadratic programming (SQP) exploit the low dimensionality of the subspace of the decision variables, and have been very successful for a wide variety of process applications. However, further development is needed for improving the efficient large-scale use of these tools. In this study we develop an improved SQP algorithm decomposition with coordinate bases that includes an inexpensive second-order correction term. The resulting algorithm is 1-step Q -superlinearly convergent. More importantly, though, the resulting algorithm is largely independent of the specific decomposition steps. Thus, the inexpensive factorization of the coordinate decomposition can be applied in a reliable and efficient manner. With this efficient and easy-to-implement NLP strategy, we continue to improve the performance of the optimization algorithm by exploiting the mathematical structure of existing process engineering models. Here we consider the tailoring of a reduced Hessian method for the block tridiagonal structure of the model equations for distillation columns. This approach is applied to the Naphthali—Sandholm algorithm implemented within the UNIDIST and NRDIST programs. Our reduced Hessian SQP strategy is incorporated with only minor changes in the program's interface and data structures. Through this integration, reductions of 20–80% in the total CPU time are obtained compared to general reduced space optimization; an order of magnitude reduction is obtained when compared to conventional sequential strategies. Consequently, this approach shows considerable potential for efficient and reliable large-scale process optimization, particularly when complex Newton-based process models are already available.