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