Advanced Optimization Methods / Conic Optimization

Course guarantor:

Jakub Mareček

Lecturer:

Jakub Mareček

Tutor:

Jakub Mareček

Supervisor:

Department of Applied Mathematics

Synopsis:

Motivating examples. Conic optimization: Convex cones, Primal and dual conic problems, Spectrahedra and LMIs, Spectrahedral shadows, SDP duality, Numerical SDP solvers, Exact SDP solvers. Finite-dimensional polynomial optimization: Measures and moments, Riesz functional, moment and localizing matrices, Lasserres hierarchy, Global optimum recovery, Software interfaces, Back to the motivating examples. Infinite-dimensional polynomial optimization. Extensions to time-varying coefficients. The motivating examples revisited.

Requirements:

Syllabus of lectures:

1. Motivating examples. Algebraic modelling languages.

2. Conic optimization: Convex cones, Primal and dual conic problems, Spectrahedra and LMIs, Spectrahedral shadows.

3. SDP duality, Numerical SDP solvers.

4. Exact SDP solvers and associated algebraic geometry.

5. Finite-dimensional polynomial optimization: an overview.

6. Measures and moments, Riesz functional.

7. Commutative POP: moment and localizing matrices, Lasserres hierarchy.

8. Non-commutative POP: moment and localizing matrices, NPA hierarchy.

9. Global optimum recovery.

10. Infinite-dimensional polynomial optimization.

11. Optimal control.

12. Extensions to time-varying coefficients.

13. The motivating examples revisited.

Syllabus of tutorials:

The labs cover some of the popular packages:

1. Cvxpyy

2. Yalmip

3. Yalmip

4. Ncpol2sdpa

5. Ncpol2sdpa

6. TSSOS

7. TSSOS

8. NCTSSOS

9. momgraph

10. POCP

Study Objective:

Study materials:

Anjos, Miguel F., and Jean B. Lasserre, eds. Handbook on semidefinite, conic and polynomial optimization. Vol. 166. Springer Science & Business Media, 2011. Burgdorf, Sabine, Igor Klep, and Janez Povh. Optimization of polynomials in non-commuting variables. Vol. 2. Berlin: Springer, 2016.

Note:

The course is presented in Czech language.

Further information:

https://cw.fel.cvut.cz/b251/courses/bqm36pmo/start

Time-table for winter semester 2025/2026:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed	roomKN:A-311 Mareček J. 09:15–10:45 (lecture parallel1) Karlovo nám. roomKN:A-311 Mareček J. 11:00–12:30 (lecture parallel1 parallel nr.101) Karlovo nám.
Thu
Fri

Time-table for summer semester 2025/2026:

Time-table is not available yet

The course is a part of the following study plans:

• Quantum Informatics (elective course)