# Large-Scale Convex Optimization

Graduate course (7.5 credits) given at the Department of Automatic Control, November to December 2015. If you want to follow the course, send Pontus Giselsson (course responsible) an email to be added to the course email list.

#### News

**Deadline for Handin 5 is postponed to Dec 18.**

**The exam can now be picked up at Eva Westin's or Mika Nishimura's office (5th floor M-building). It is a 48 hour take-home exam. Please contact them some time in advance to schedule the pickup. The solutions should be handed in to Eva or Mika within 48 hours, and a scanned version should be sent to me via email. If you are not present in Lund, you can get the exam via email. Contact me some time in advance to arrange this.**

**Schedule**

We have two lectures and one exercise session per week, starting November 2nd. All meetings will be held in Seminarierum M2112B (M-building, second floor).

Lectures: Mondays 13-15 and Wednesdays 10-12.

Exercise sessions: Thursdays 13-15.

#### 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).