Exploring computational sustainability via differential variational inequalities.

摘要

Sustainability is a widely accepted paradigm for a better future in governmental as well as non-governmental organizations. Computational sustainability is a rapidly growing area of study and has received a surge of interest for modeling and computing the solutions of sustainability problems. In this dissertation, we explore computational sustainability. The focus is to provide a solid theoretical foundation for computational sustainability and apply it to sustainability problems including (i) renewable resource management (ii) supply chain management, and (iii) environmental management.;Underlying frameworks to tackle computationally challenging sustainability problems include optimal control theory, dynamic game theory in the formalism of a differential variational inequality (DVI), and robust optimization. We aim to make a contribution in the direction of computational sustainability since the potentialities of those frameworks to this field has yet to be fully explored. Our approach to dealing with sustainability problems is based on the expression of the robust model as a variational inequality or a DVI, which in turn may be solved using methods such as successive linearization, fixed-point, complementarity, and gap function/projection. This is a significant departure from the usual dynamic programming approach and should be of intrinsic interest since it allows to include many behavioral features that make the mathematical model of sustainability problem more realistic.