Large-scale Optimization
Algorithms for solving large-scale, continuous, optimization problems — from fundamentals to advanced techniques.
Instructor: Sebastian Mair and Jens Sjölund
Overview
This PhD course (FTN0452, 6 hp) addresses algorithms for solving large-scale continuous optimization problems. Students develop understanding of problem challenges and mathematical structures enabling efficient solver implementation through theoretical knowledge and practical assignments.
Topics include numerical linear algebra, first-order methods for unconstrained and constrained optimization, duality, automatic differentiation, and related techniques.
Format
- 10 lectures
- 3 hand-in assignments with peer review
- Optional 3 hp project
Prerequisites
Undergraduate multivariate calculus and linear algebra; scientific programming experience (Python, MATLAB, or Julia). Prior optimization coursework is advantageous but not required.
Learning outcomes
Upon completion, students should be able to:
- Formulate scientific and engineering problems as optimization problems
- Identify mathematical properties (smoothness, convexity) and computational advantages (sparsity)
- Describe and explain the principles of covered algorithms
- Analyse, implement, and tailor optimization methods to large-scale problems
- Provide constructive peer feedback on assignments