Advanced Optimization Methods / Conic Optimization
Semestr:
Range: 2P+2C
Completion:
Credits: 6
Programme type: Master
Study form: Fulltime
Course language: Czech
Summary:
The course introduces conic optimization as a unifying framework for the study of a wide range of optimization problems.
Keywords:
Conic optimization, semidefinite programming, polynomial optimization
Course syllabus:
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, Lasserre’s 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.
Seminar syllabus:
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
Literature:
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.