Mathematical optimization provides a unifying framework for studying issues of rational decision-making, optimal design, effective resource allocation and economic efficiency. It is therefore a central methodology of many business-related disciplines, including operations research, marketing, accounting, economics, game theory and finance. In many of these disciplines, a solid background in optimization theory is essential for doing research.
This course provides a rigorous introduction to the fundamental theory of optimization. It examines optimization theory in deterministic settings, including optimization in Rn and optimization over time (optimal control). The course emphasizes the unifying themes (optimality conditions, Lagrange multipliers, convexity, duality) that are common to all these areas of mathematical optimization. Applications from problem areas in which optimization plays a key role are also introduced. The goal of the course is to provide students with a foundation sufficient to use basic optimization in their own research work and/or to pursue more specialized studies involving optimization theory.
The course is open to all students, but it is designed for entering doctoral students. The prerequisites are calculus, linear algebra and some familiarity with real analysis. Other concepts (e.g., vector spaces) are developed as needed throughout the course.