Projected Dynamical Systems and Variational Inequalities with Applications

Equilibrium is a concept used in operations research and economics to understand the interplay of factors and problems arising from competitive systems in the economic world. The problems in this area are large and complex and have involved a variety of mathematical methodologies. In this monograph, the authors have widened the scope of theoretical work with a new approach to previous work in variational inequality theory. While most classical work in this area is static, the introduction to the theory of projected dynamical systems will allow many real-life dynamic situations and problems to be handled and modelled. This text includes: a new theoretical approach, "projected dynamical system", which allows the researcher to model real-life situations more accurately; new mathematical methods allowing researchers natural, financial and human (real-life) situations in competitive equilibrium problems; and the computational and numerical methods for the implementation of the methods and theory discussed in the book. Stability analysis, algorithms and computational procedures are offered for each set of applications.