Resumen de Mathematical programming based approaches for classes of complex network problems: economical and sociological applications
Stefano Nasini
The thesis deals with the theoretical and practical study of mathematical programming methodologies to the analysis complex networks and their application in economic and social problems. More specifically, it applies models and methods for solving linear and integer programming problems to network models exploiting the matrix structure of such models, resulting in efficient computational procedures and small processing time. As a consequence, it allows the study of larger and more complex networks models that arise in many economical and sociological applications. The main efforts have been addressed to the development of a rigorous mathematical programming based framework, which is able to capture many classes of complex network problems. Such a framework involves a general and flexible modeling approach, based on linear and integer programmin, as well as a collection of efficient probabilistic procedures to deal with these models. The computer implementation has been carried out by high level programming languages, such as Java, MatLab, R and AMPL. The final chapter of the thesis introduced an extension of the analyzed model to the case of microeconomic interaction, providing a fruitful mathematical linkage between its optimization-like properties and its multi-agents properties. The theoretical and practical use of optimization methods represents the trait-de-union of the different chapters. The overall structure of the thesis manuscript contains three parts: Part I: The fine-grained structure of complex networks: theories, models and methods; Chapter 1 and Chapter 2. Part II: Mathematical Programming based approaches for random models of network formation; Chapter 3, Chapter 4 and Chapter 5. Part III: Strategic models of network formation. Chapter 6. Results of this research have generated four working papers in quality scientific journals: one has been accepted and three are under review. Some results have been also presented in four international conferences.
