New approaches to a reduced Hessian successive quadratic programming method for large-scale process optimization

This thesis describes new methods for a reduced Hessian Successive Quadratic Programming (rSQP) algorithm for large-scale process optimization. Over the past fifteen years, the Successive Quadratic Programming algorithm and the rSQP algorithm in particular, has been applied to a wide variety of problems in process engineering. Designed for large NLP problems with few degrees of freedom, the rSQP approach requires only projected second derivative information which can often be approximated efficiently with quasi-Newton update formulae. The enhancements described in this thesis improve the efficiency, performance, and reliability of these algorithms and preserve the desirable convergence properties shown in earlier studies.;A trust region approach is implemented to improve the convergence of the rSQP algorithm for problems which have poor initial curvature information. This new approach restricts the step size of the Newton direction to move the initial search directions towards a steepest descent direction. This work is extended by modifying the solution strategy for the Quadratic Programming (QP) subproblem. This new adjoint approach allows for the partial solution of the QP subproblem which reduces the solution time for the overall rSQP algorithm for some problems. A large set of test problems are then solved with the new algorithm in the GAMS system. The results show that the rSQP algorithm is both robust and efficient.;To overcome the combinatorial expense of solving the QP subproblem with an active-set method, we introduce an interior-point. The basic primal-dual interior point method is described and results are shown for some medium sized industrial test problems. Some larger test problems are then presented which offer a comparison of two active-set method QP solvers, QPKWIK and QPOPT, with the interior-point solver. This comparison shows that an interior point method can solve large highly-constrained problems faster than traditional active set methods.;Finally, a new approach to implementing the rSQP algorithm is described. This approach takes advantage of some object-oriented programming concepts in the C++ programming language to make the rSQP code more understandable and maintainable than the current, procedure-oriented, Fortran 77 code. The goals of this new implementation are outlined and some examples of C++ objects for the rSQP algorithm are described.