Advanced Optimization Methods / Conic Optimization

Course guarantor:

Lecturer:

Tutor:

Supervisor:

Department of Computer Science

Synopsis:

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 primarily intended for students of QNI (Quantum Computer Science, Kvantová informatika, FIT), but open also to MPOI (Otevřená informatika, FEL).

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: