IKT720 - Optimization

Overview

This course aims at building familiarity with optimization in general, but the focus is on convex optimization. After studying the theory of convex sets, functions, and problems, the theory of duality is developed. Afterwards, the main principles of iterative optimization algorithms are presented both for unconstrained and constrained problems. The student also learns to use CVX as a tool to solve convex optimization problems in proof-of-concept tasks.

Prerequisites

Linear algebra, basic analysis, MATLAB programming.

Syllabus

1. Introduction
2. Convex sets
3. Convex functions
4. Convex problems
5. Lagrangian duality theory
6. First-order optimization methods for unconstrained problems
7. Second-order optimization methods for unconstrained and linearly constrained problems
8. Interior point methods

Main Bibliography

1. Stephen P. Boyd, and Lieven Vandenberghe. Convex optimization. Cambridge university press, 2004.
2. Yurii Nesterov. Lectures on convex optimization. Springer, 2018.