Graduate course (7.5 credits) given at the Department of Automatic Control, November to December 2015. Developed by Pontus Giselsson.

Textbooks

• [HiL93]: Convex Analysis and Minimization Algorithms I (link) and II (link). J.-B. Hiriart-Urruty and C. Lemaréchal. 1993.
• [HiL01]: Fundamentals of Convex Analysis. J.-B. Hiriart-Urruty and C. Lemaréchal. 2001. This is a shorter version of the above book series.
• [BaC11]: Convex Analysis and Monotone Operator Theory in Hilbert Spaces. H. H. Bauschke and P. L. Combettes. 2011. (Should be possible to download from within LU:s net.)
• [RyB15]: Primer on Monotone Operators. E. Ryu and S. Boyd. 2015.
• [BoV04]: Convex Optimization. S. Boyd and L. Vandenberghe. 2004.

Lectures

• 1. Convex sets
• 2. Convex functions
• 3. Subdifferentials
• 4. Conjugate functions
• 5. Duality
• 6. Operator properties
• 7. Subdifferential operator properties
• 8. Important operators
• 9. Optimality conditions/algorithms
• 10. Algorithms
• 11. Algorithms
• 12. Optimization modeling

Reading

• Lecture 1.
  • [HiL93]: Sections III.1, III.2.1, III.4, III.5 (also III.3 will be useful later)
  • [HiL01]: Sections A.1, A.2.1, A.4, A.5 (also A.3 will be useful later)
• Lecture 2.
  • [HiL93]: Chapter IV (and V optional)
  • [HiL01]: Chapter B (and C optional)
• Lecture 3.
  • [HiL93]: Chapter VI (Chapter XI also useful, need Chapter X for this, which is covered in next lecture)
  • [HiL01]: Chapter D
• Lecture 4:
  • [HiL93]: Chapter X
  • [HiL01]: Chapter E
• Lecture 5: Results are consequences of previous material, summarized in:
  • [BaC11]: Chapter 15
• Lecture 6:
  • [RyB15]: Sections 3,4,5.
  • ([BaC11]: Chapters 4,5.)
• Lecture 7:
  • [HiL93]: Chapter X.4.
  • [HiL01]: Chapter E.4.
  • [RyB15]: Section 9.
• Lecture 8:
  • [RyB15]: Section 6.
• Lecture 9-11:
  • [RyB15]: Section 6, 7, 8.

Exercises

• Convex sets. Convex functions. Subdifferentials. (Handin: exercises 2,7,8. Due Nov 12)
• Conjugate functions. Duality. (Handin: exercises 4 and 7. Due Nov 19)
• Operator properties. (Handin 3,4,5. Due Nov 26)
• Important operators. Algorithms. (Handin 1,2. Due Dec 3)
• Algorithms. (Handin 1 and 2 or 3, i.e., you can choose between 2 and 3. Due Dec 18)

Exam

More information to come.

Project (+3 credits)

It is possible to add a project to the course. Projects can be done in groups of 1-3 persons. You could either come up with your own project (perhaps in relation to your research) or choose from a list of suggested projects (to come).