Mathematic Colloquium: Exploring the Systematic Framework for Computational Sustainability
4:10 pm Neill 5W
Dr. Sung Hoon Chung
Computational Sustainability is a rapidly growing interdisciplinary field that has received a surge of interest for modeling and computing the solutions of complex sustainability problems. The salient features in sustainability problems include 1) dynamics, 2) competition, and 3) uncertainty, and consideration of all such features makes the mathematical model realistic and, simultaneously, computationally very challenging. This talk presents a systematic framework for Computational Sustainability, based on novel mathematical models, effective numerical algorithms, and analytical tools via mathematical disciplines such as nonlinear optimization, variational inequality, optimal control, stochastic programming, and game theory. The systematic framework is intended to serve as a decision support tool in the development of policies for balancing environmental, economic, and societal needs, in support of sustainable development and a sustainable future. The range of sustainability problems includes optimal renewable resource allocation, cascading ocean disaster management, sustainable transportation networks, and environmental operations management. My approach to modeling and computing the solutions of complex sustainability problems is based on the expression of the model as dynamic games and the introduction of differential variational inequality (DVI) formalism as a solution methodology. Interest in the DVI formalism for dynamic games stems from a desire to replicate the success realized in the application of finite dimensional variational inequality theory to the study of static games. In particular, the historic emphasis of differential game theory on the Hamilton-Jacobi partial differential equation and dynamic programming can be replaced by efficient methods that employ the notions of fixed point, complementarity, interior point, and projection in the context of the DVI formalism. This is a significant departure from the usual dynamic programming approach and should be of intrinsic interest since it allows the inclusion of many behavioral features that makes the mathematical models more realistic and, therefore, provides ample opportunity to generate insights into complex sustainable management systems. This approach also provides analytical tools and qualitative results such as decision rules derived from necessary conditions, existence and uniqueness of the solution, comparative dynamics, and sensitivity analysis to complement numerical solutions. This talk also covers the application of the proposed framework to several sustainability problems, and introduces some future works.