Mixed integer nonlinear and nonconvex optimization of structured process systems

Current algorithms for Mixed Integer Non Linear Programming problems have limitations in the size of problems that they can solve and in the handling of nonconvex functions. This thesis focuses in the development of algorithms for the solution of convex MINLP problems as well as in the solution of nonconvex Non Linear Programming problems that involve bilinear and linear fractional terms. The structure of these problems is exploited to obtain efficient solution methods.; An algorithm for the solution of convex MINLP problems is first developed. This algorithm consists of a dynamic branch and bound search in which LP subproblems are solved at intermediate nodes and Non Linear Programming subproblems at integer nodes. Information from the solution of these NLP problems is employed to generate linear approximations used in the branch and bound search. A new type of partial surrogate constraints is presented in which the linear substructures of the model are exploited.; Nonconvex NLP problems that involve linear fractional and bilinear terms are considered next. A linear fractional model for the optimization of Heat Exchanger Network is presented. A deterministic global optimization is developed in which the key feature is a nonlinear convex underestimator problem. This problem uses nonlinear and linear estimators and the relation between these estimators is established. Additional estimator functions are generated through the use of projections of the feasible region. A spatial branch and bound search is conducted to obtain the global optimum. These ideas are generalized for the solution of NLP models that involve bilinear and linear fractional terms.; Finally, the solution of other structured nonconvex problems is also presented. The optimization of process networks involving multicomponent streams is considered. A relation between the different type of formulations commonly used is established through reformulation and linearization techniques. A tight linear relaxation is obtained that can be employed within the framework of the global optimization algorithm presented in this thesis. The solution of separation networks with mixed products and sharp separators is discussed. Applications from different engineering fields are also given with particular relaxations that exploit the mathematical structure of the models. Extensive numerical results are given throughout the thesis.