Nonlinear process optimization with many degrees of freedom

This thesis addresses efficient methods in solving large-scale nonlinear problems with many degrees of freedom. Applications of large-scale nonlinear optimization problems with many degrees of freedom have become more common in the process industries, especially in the area of process operations. However, most widely used nonlinear programming (NLP) solvers are designed for the efficient solution of problems with few degrees of freedom. The new barrier algorithm also known as Interior Point Optimization (IPOPT), which follows a primal-dual interior point approach is designed for solving large-scale optimization problems with many degrees of freedom and many potential active constraints set. These large-scale nonlinear optimization problems are nonconvex in nature hence solving for optimal solutions can be extremely challenging. Applicable solvers for these problems need to exploit sparsity in the problem structure which usually requires second order information from the optimization model. Moreover, these methods also need to handle computational difficulties such as redundant (i.e., degenerate) constraints and lack of positive definiteness in the reduced Hessian matrix.; In this research, we focused on solving these large-scale problems based on good initialization strategies and efficient optimization techniques. To demonstrate its effectiveness on process applications, we considered a class of large-scale blending and data reconciliation problems, both of which contained nonlinear mass balance constraints and process properties and compared IPOPT's solver robustness, improved convergence and computational speed with other state of the art popular NLP algorithms. Secondly we evaluated the IPOPT algorithm as one of the solvers in the Rigorous Online Modeling with equation based optimization tool (ROMeo(TM)) to compare the solver's performances with ROMeo(TM)'s in-house successive quadratic programming (SQP) solver OPERA.; Our final work was performed in developing a new data reconciliation tool, DataRec, designed for reconciling linear data reconciliation measurements problems. The DataRec algorithm follows a Lagrange multiplier method with a modified gross error detection strategy. It uses the Fair function (M-estimator) with an accurate solution and an iterative trust region method for its convergence properties. Since there is no negative curvature of the Hessian matrix i.e., "no hard case", a Levenberg-Marquardt parameter gamma, which is inversely related to the trust region radius Delta is used. The algorithm is tested on several data reconciliation models and results are presented.