Object-oriented approaches to large-scale nonlinear programming for process systems engineering

This thesis concerns the numerical solution of large-scale NonLinear Programs (NLPs) for process systems engineering and other types of related optimization problems. Described here is a new approach for modeling and implementating reduced space Successive Quadratic Programming (rSQP) algorithms. An object-oriented methodology is used to develop a framework for rSQP called rSQP++ in C++. The goals for rSQP++ are quite lofty. The rSQP++ framework is being designed to incorporate many different SQP algorithms and to allow external configuration of specialized linear algebra objects such as vectors, matrices and linear solvers. In addition, it is possible for the client to modify the SQP algorithms to meet other specialized needs without having to touch any of the source code within the rSQP++ framework.; Another aspect to this thesis is devoted to finding ways to extend rSQP to NLPs with more degrees of freedom. In this vein, a new dual space, active set, Schur complement Quadratic Programming (QP) solver called QPSchur is described. Not only has QPSchur been shown to be more computationally efficient than several other QP solvers on many problems, but its ability to be externally configured with specialized linear algebra options is also demonstrated. Also, strategies for reducing the cost of quasi-Newton Hessian approximations are investigated for use in rSQP. A compact limited memory BFGS approximation has been implemented and explored and a projected BFGS approach in the space of the superbasic variables has been investigated. Numerical results demonstrate the dramatic impact these two measures can have in reducing the computation time.; This work is demonstrated on several different NLPs from various application areas. The effectiveness of using QPSchur as the QP solver in a Model Predictive Control (MPC) application for a specialized paper process is proven. This new MPC controller is shown to be two orders of magnitude faster than a currently used MPC controller in Matlab. Nonlinear MPC (NMPC) is also considered. The example process is the difficult Tennessee Eastman challenge problem. Here rSQP++ is compared to an interior-point solver IPOPT. Some of the tradeoffs between active set and interior point NLP solvers for use with NMPC are demonstrated on this difficult problem.; Finally, the use of rSQP for PDE constrained optimization is explored, along with its extension to distributed memory, parallel computing environments. Here, a “Tailored Approach” interface and a PDE simulation code MPSalsa is developed and used to solve a Chemical Vapor Decomposition (CVD) design problem in an order of magnitude less time than a currently used “Black Box” approach. Open questions for PDE constrained optimization are discussed and the difficulties in allowing the parallelization of rSQP++ are described. To address the difficulties in allowing optimization codes to exploit special computing environments without be taken over, a new and novel object-oriented design for vectors and vector reduction/transformation operators is described in great detail. Adopting such a design will allow the basic linear algebra operations used in an optimization code to be taken over by a specialized application without having to touch or even recompile one line of core code in the optimization algorithm.