Enrolment guidelines

This is a toolbox course where 80% of the seats are reserved for PhD students enrolled at the Faculty of SCIENCE at UCPH and 20% of the seats are reserved for PhD students from other Danish Universities/faculties (except CBS). Seats will be allocated on a first-come, first-served basis and according to the applicable rules.

Anyone can apply for the course, but if you are not a PhD student at a Danish university (except CBS), you will be placed on the waiting list until enrollment deadline. After the enrollment deadline, available seats will be allocated to applicants on the waiting list.

Aim and Content
Numerical optimization is a key computer tool across various fields, including image processing, machine learning, bioinformatics, economics, etc. It addresses diverse problems, Maximum Likelihood or Maximum a Posteriori parameter estimation, inverse kinematics in robotics and many optimization problems in imaging, denoising, segmentation, reconstruction etc. for instance in medical imaging.

This course will equip PhD students with a set of numerical optimization techniques, making it an excellent addition for those from various scientific backgrounds. It covers the fundamental theory and practical implementation of these methods, emphasizing deep understanding, mathematical derivation, and programming best practices. Students will also be trained on practical examples from the research directions pursued in the IMAGE section.

Learning outcomes

Knowledge:
1. Line search Gradient descent and Newton Method, Trust Regions, Gauss-Newton, Levenberg-Marquardt, simple constrained optimization including linear programming (simplex and interior point methods) etc.

Skills:
2. Ability to use numerical optimization solutions in practice
3. Ability to use optimization toolboxes such as Python SciPy optimisation packages as well as others.

Competences:
4. Identify practical situations where numerical optimisation is needed.
5. Ability to formulate a problem as a numerical optimisation task.
6. Ability to choose a suitable optimization method

Target Group
Ph.D. students in computer science, mathematics, chemistry, economics and physics

Recommended Academic Qualifications
M.Sc in computer science, mathematics, chemistry, economics and physics or equivalent.

Research Area
Computer Science, mathematics, chemistry, economics and physics.

Teaching and Learning Method
5 full days with morning lecture and afternoon exercises

Type of Assessment
One or two large take home assignments.

Literature
Numerical Optimization, J. Nocedal and S. J. Wright. Springer. Course Notes.

Course coordinator
François Lauze, Associate Professor, DIKU.

Guest Lecturer
Bernhard Kerbl, Assistant Professor, DIKU

Dates
Block 4, April 20-24, 2026

Expected frequency
Once a year, block 4 unless there is enough interest from students, then we will run a new occurrence in the beginning of block 2.

Course location
North Campus or Frederiksberg Campus

Registration
Registration with waiting list

Deadline for registration
4 weeks before course starts. If seats are available late registration might be accepted (with a cap on 30 participants)

Course fee
• Participant fee: 0 DKK
• PhD student enrolled at SCIENCE: 0 DKK
• PhD student from Danish PhD school Open market: 0 DKK
• PhD student from Danish PhD school not Open market: 3000 DKK
• PhD student from foreign university: 3000 DKK
• Master’s student from Danish university: 0 DKK
• Master’s student from foreign university: 3000 DKK
• Non-PhD student employed at a university (e.g., postdocs): 3000 DKK
• Non-PhD student not employed at a university (e.g., from a private company): 8400 DKK

Cancellation policy
• Cancellations made up to two weeks before the course starts are free of charge.
• Cancellations made less than two weeks before the course starts will be charged a fee of DKK 3.000
• Participants with less than 80% attendance cannot pass the course and will be charged a fee of DKK 5.000
• No-show will result in a fee of DKK 5.000
• Participants who fail to hand in any mandatory exams or assignments cannot pass the course and will be charged a fee of DKK 5.000

Course fee and participant fee
PhD courses offered at the Faculty of SCIENCE have course fees corresponding to different participant types.
In addition to the course fee, there might also be a participant fee.
If the course has a participant fee, this will apply to all participants regardless of participant
type – and in addition to the course fee.

Disclaimer:
DDSA has explicit permission from Arcanic and the owners of the https://phdcourses.dk/ website to display the courses on ddsa.dk.