| A complex system is a collection of processes, subsystems, or components that (1) possess dissimilar mathematical structure or representation; (2) are connected to each other, possibly in nonlinear ways and/or by a network; or (3) perform in the presence of noncomparable and perhaps conflicting criteria or objectives. The study of complex systems involves answering questions about the whole system, the parts that make it up, and the relationships between these parts. For the system to operate properly, all processes, subsystems, and components must be designed, tuned, and coordinated to work together. Often it is necessary to decompose the system and optimize the subsystems individually and independently to obtain a solution.;This research studies ways to improve the adaptability and flexibility of complex system modeling and solution methods. Two distinct methodologies are proposed or advanced in this regard. The first is the development of Network Target Coordination (NTC) which models the system using nonhierarchical relationships between subproblems. NTC allows subproblems to represent disparate organizational views of the system within the same model, such as by physical components or by engineering disciplines. The nonhierarchical formulation of the system also permits new subsystems to be added to the model in a straightforward manner, allowing designers to make changes to the system with a minimal amount of difficulty.;The second area of study is the application of Multiparametric Programming (MPP) to complex system design. Many elements of a system do not fall under the classification of variables to be optimized, but are nevertheless quantities that are subject to change. MPP techniques are melded with NTC so that parameters can be included in complex system models, allowing designers to more easily and capably deal with changes and alterations to system properties. This study involves proving duality relationships for parametric nonlinear programs and designing convergent parametric subgradient algorithms. Several examples are presented demonstrating these methods and showing how parameters can enhance system design. |
