# Large-Scale Convex Optimization

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).