Course: Convex Optimisation

Professor: Cagil Kocyigit

ECTS: 2

Aims:

Convex optimization is a fundamental branch of applied mathematics that has applications in almost all areas of operations research, engineering, the basic sciences and economics. For example, it is not possible to fully understand support vector machines in statistical learning, nodal pricing in electricity markets, the fundamental welfare theorems in economics, or Nash equilibria in two-player zero-sum games without understanding the duality theory of convex optimization.

The course primarily focuses on techniques for formulating decision problems as convex

optimization models that can be solved with existing software tools. The exact formulation of an

optimization model often determines whether the model can be solved within seconds or only within days, and whether it can be solved for ten variables or up to 10^6 variables. The course does not address optimization algorithms but covers the theory that is necessary to follow advanced courses on optimization algorithms.

Learning Objectives:

By the end of the course, the student must be able to:

• Formalize decision problems in operations research, engineering and economics as mathematical optimization models
• Solve the resulting models with off-the-shelf optimization software and interpret the results
• Assess / evaluate the computational complexity of different classes of optimization problems and use modelling techniques to make specific optimization problems more tractable