Fundamentals of Optimization

Participation Prerequisites

By nature of the subject, the content of this course is mathematical (although illustrated with business problems). It aims to be self-contained, but students should 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

Course Content

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:

1. Structure of an optimization problem
2. Deterministic versus stochastic optimization
3. Continuous versus discrete optimization
4. Constrained versus unconstrained optimization
5. Fundamentally important concepts like convexity, duality, complexity, total unimodularity, ...
6. 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. We will leverage ChatGPT to support us in formulating optimization problems and to generate code.

Intended Learning Outcomes and Competencies

• 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.

Instruction Type

On-campus study

Form of Examination

100%: individual report (word limit 2,000)

Literature

There is no course textbook. Relevant references will be provided during the course.