SOLVING TWO-LEVEL OPTIMIZATION PROBLEMS WITH APPLICATIONS TO ROBUST DESIGN AND ENERGY MARKETS

This dissertation provides efficient techniques to solve two-level optimization problems. Three specific types of problems are considered. The first problem is robust optimization, which has direct applications to engineering design. Traditionally robust optimization problems have been solved using an inner-outer structure, which can be computationally expensive. This dissertation provides a method to decompose and solve this two-level structure using a modified Benders decomposition. This gradient-based technique is applicable to robust optimization problems with quasiconvex constraints and provides approximate solutions to problems with nonlinear constraints. The second types of two-level problems considered are mathematical and equilibrium programs with equilibrium constraints. Their two-level structure is simplified using Schur's decomposition and reformulation schemes for absolute value functions. The resulting formulations are applicable to game theory problems in operations research and economics. The third type of two-level problem studied is discretely-constrained mixed linear complementarity problems. These are first formulated into a two-level mathematical program with equilibrium constraints and then solved using the aforementioned technique for mathematical and equilibrium programs with equilibrium constraints. The techniques for all three problems help simplify the two-level structure into one level, which helps gain numerical and application insights. The computational effort for solving these problems is greatly reduced using the techniques in this dissertation. Finally, a host of numerical examples are presented to verify the approaches. Diverse applications to economics, operations research, and engineering design motivate the relevance of the novel methods developed in this dissertation

Emerging Themes and Future Directions of Multi-Sector Nexus Research and Implementation

Water, energy, and food are all essential components of human societies. Collectively, their respective resource systems are interconnected in what is called the “nexus”. There is growing consensus that a holistic understanding of the interdependencies and trade-offs between these sectors and other related systems is critical to solving many of the global challenges they present. While nexus research has grown exponentially since 2011, there is no unified, overarching approach, and the implementation of concepts remains hampered by the lack of clear case studies. Here, we present the results of a collaborative thought exercise involving 75 scientists and summarize them into 10 key recommendations covering: the most critical nexus issues of today, emerging themes, and where future efforts should be directed. We conclude that a nexus community of practice to promote open communication among researchers, to maintain and share standardized datasets, and to develop applied case studies will facilitate transparent comparisons of models and encourage the adoption of nexus approaches in practice

Emerging Themes and Future Directions of Multi-Sector Nexus Research and Implementation

Water, energy, and food are all essential components of human societies. Collectively, their respective resource systems are interconnected in what is called the “nexus”. There is growing consensus that a holistic understanding of the interdependencies and trade-offs between these sectors and other related systems is critical to solving many of the global challenges they present. While nexus research has grown exponentially since 2011, there is no unified, overarching approach, and the implementation of concepts remains hampered by the lack of clear case studies. Here, we present the results of a collaborative thought exercise involving 75 scientists and summarize them into 10 key recommendations covering: the most critical nexus issues of today, emerging themes, and where future efforts should be directed. We conclude that a nexus community of practice to promote open communication among researchers, to maintain and share standardized datasets, and to develop applied case studies will facilitate transparent comparisons of models and encourage the adoption of nexus approaches in practice

Emerging themes and future directions of multi-sector nexus research and implementation

Water, energy, and food are all essential components of human societies. Collectively, their respective resource systems are interconnected in what is called the “nexus”. There is growing consensus that a holistic understanding of the interdependencies and trade-offs between these sectors and other related systems is critical to solving many of the global challenges they present. While nexus research has grown exponentially since 2011, there is no unified, overarching approach, and the implementation of concepts remains hampered by the lack of clear case studies. Here, we present the results of a collaborative thought exercise involving 75 scientists and summarize them into 10 key recommendations covering: the most critical nexus issues of today, emerging themes, and where future efforts should be directed. We conclude that a nexus community of practice to promote open communication among researchers, to maintain and share standardized datasets, and to develop applied case studies will facilitate transparent comparisons of models and encourage the adoption of nexus approaches in practice