Mathematical optimization in Operations Research
Operations Research (O.R.) is the application of scientific and mathematical methods to the study and analysis of problems involving complex systems (according to The Institute for Operations Research and the Management Sciences). Among many mathematical methods and tools in O.R., the most fundamental is the concept of optimization. It is to search for the best choice among possible alternatives under certain conditions and constraints. In the mathematical language, it is to maximize or minimize a given objective function by controlling decision variables under the set of constraints. Optimization theory is also a part of applied mathematics, and is widely employed in academic disciplines that deal with mathematical modeling of human decision making. In particular, it plays an essential role in economics for its descriptions of economic decision making and valuation.
In this lecture, students will learn the theories of mathematical optimization as methods in O.R. The lecture starts with providing an overview of O.R. with an emphasis on optimization methods. It moves on to the theory of static optimization. The third part of the lecture discusses the theory of dynamic optimization.