This book offers a comprehensive analysis of dynamic networks and evolutionary variational inequalities, a topic of growing prominence in the study of networks. The extraordinary importance of networks in finance, mathematics, computer science and other areas is well known but the relatively new concept of ‘dynamic’ networks is less well understood. They become dynamic when the constitutive elements of the phenomena associated with the fixed geometry of networks are considered to be evolving over time. Patrizia Daniele offers many numerical examples to illustrate the issues discussed and provides a broad appendix to enrich this challenging but deeply informative book.
Researchers, students and practitioners in the areas of finance, economics, computer science, and mathematics will find this volume an indispensable resource in understanding the use and development of networks in their disciplines.
1. Introduction 2. The Traffic Equilibrium Problem 3. Evolutionary Spatial Price Equilibrium 4. The Evolutionary Financial Model 5. Projected Dynamical Systems A. Definitions and Properties B. Weak Convergence C. Generalized Derivatives D. Variational Inequalities E. Quasi-Variational Inequalities F. Infinite Dimensional Duality Bibliography Index