Fundamentals of Optimization

Optimization is important to many applications in business, be that finance, operations, marketing or others. This course aims to provide a broad overview of the concepts that underpin optimization to help students to gain an understanding of what type of optimization problem they may be dealing with in their studies, and how this could be tackled.

Coverage includes:

• Structure of an optimization problem
• Deterministic versus stochastic optimization
• Continuous versus discrete optimization
• Constrained versus unconstrained optimization
• Fundamentally important concepts like convexity, duality, complexity, total unimodularity, ...
• Introduction to various techniques including linear and non-linear mathematical programming, (approximate) dynamic programming for control problems, optimal learning

We will not go overly deep into the topics due to time constraints; instead, the focus is on imparting an intuitive understanding of optimization techniques and of structures that can be exploited. The intention is to make this course useful and relevant to any students who face some form of optimization problem and who do not yet have received formal training in optimization.

Ability to formulate and recognize the type of different optimization problems

Ability to explain in high-level terms how different optimization approaches work

Ability to discuss advantages and disadvantages of different optimization approaches

There is no course textbook. The books below merely illustrate sources that students may find useful; various tutorial papers and examples of research papers that make use of the covered techniques will be used within the course. Stephen Boyd and Lieven Vandenberghe. Convex Optimization. Cambridge, 2004Warren Powell. Approximate Dynamic Programming. 2011. Wiley

Mostly delivered in lectures, mixed with in-class exercises and quizzes

80%: individual report (word limit 2,000)

20%: participation in class

By nature of the subject, the content of this course is mathematical (although illustrated withbusiness problems). It aims to be self-contained, but studentsshould be familiar with at least high school level mathematics (e.g. gradients, basic matrix calculation, vector operations, etc).A primer document will be provided some time before the start of the course.

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