Optimization Theory and Applications

1.5 units

Optimization theory plays a fundamental role in modeling and guiding the behavior of rational consumers, firms, and regulators. This graduate course provides students a broad yet rigorous foundation in the theory and applications of optimization. It covers classical linear, nonlinear, discrete, and dynamic models; specialized methodologies of current applied research interest, including super modularity and robust optimization; applications of current research interest, including social and economic networks; and computer implementations using state-of-the-art software. See below for a detailed outline of topics covered. The course is designed for doctoral students in economics, finance, marketing, operations management, and related fields. Its objective is to help these students recognize elements of optimization models and structures in their diverse research topics, to utilize fundamental results from optimization theory to formalize, strengthen, and extend their research results, and to develop their mathematical maturity and ability to conduct rigorous proof-based research. To keep the coverage broad, only key results in each topic are presented along with their proofs. Geometric intuition is invoked whenever robust. Detailed references are provided for more specialized results. Research papers that demonstrate the applications of theory are discussed.