Reduced Hessian successive quadratic programming for large-scale process optimization

This thesis addresses the development of an efficient and robust algorithm for large-scale process optimization. The proposed method applies an inexpensive coordinate basis decomposition in conjunction with successive quadratic programming (SQP), allowing the low dimensionality of the subspace of the decision variables to be exploited. The main theoretical contribution of this work is the inclusion of a second order correction term which allows the method to incorporate additional curvature information. The resulting algorithm is largely independent of the specific decomposition method, and coordinate bases can therefore be applied in a reliable and efficient manner. Rigorous mathematical proofs are constructed which show the algorithm to be 1-step Q-superlinearly convergent.; Examination of the quadratic programming (QP) subproblem to be solved at each SQP iteration shows that the number of QP variables is typically much smaller than the total number of process variables. However, for some applications such as optimal control or multiperiod design, the number of QP variables may still be quite large. In addition, the number of QP inequalities may be large independent of the number of variable since all the bounds on the process variables are passed to the QP as simple bounds or doubly-bounded inequalities. To address these two issues, a novel QP algorithm, QPKWIK, is presented. The method is based on a dual approach to the solution of the QP optimality conditions and uses a direct update of the inverse Cholesky factor of the reduced Hessian matrix. Further, QPKWIK has been implemented so as to enhance the efficiency of the active set identification. Numerical results for a series of multiperiod problems are in agreement with theoretical predictions that the complexity of QPKWIK is O(n{dollar}sp2{dollar}) with respect to the number of QP variables. This is in contrast to most existing software which requires O(n{dollar}sp3{dollar}) operations.; The reduced Hessian successive quadratic programming algorithm developed in this thesis is particularly well suited for real-time optimization. Here, we consider a benchmark problem based on the Sunoco Hydrocracker Fractionation Plant. The model includes almost 3000 variables and over 24000 nonzero Jacobian elements; it is of realistic size and complexity to allow various operating scenarios to be considered. The numerical results indicate that our algorithm is at least as robust and about an order of magnitude faster than MINOS, the optimization algorithm originally used to solve this problem. Further, it is found to be less sensitive to a poor initial point. (Abstract shortened by UMI.)...