Number of hours
- Lectures 36.0
- Projects -
- Tutorials -
- Internship -
- Laboratory works -
- Written tests -
ECTS
ECTS 6.0
Goal(s)
The course is meant as sequel to the course "Non-smooth convex optimization methods". It treats more advanced methods and applications of convex optimization, notably structured conic programs, their solution by interior-point methods, and reformulations or approximations of common optimization problems as conic symmetric programs.
Responsible(s)
Roland HILDEBRAND
Content(s)
The subject of this half-semester course are more advanced methods in convex optimization. It consists of 6 lectures, 2 x 1,5 hours each, and can be seen as continuation of the course "Non-smooth convex optimization methods". Approximate content of each lecture:
- Linear programs / Conic programs
- Representations of linear programs
- Duality
- Symmetric cones
- Second order conic / semi-definite programming
- Liftings / Complexity
- Robust optimization
- Robust counterparts of conic programs
- Robust Linear / Second order conic / Semi-definite programs
- Interior-point methods
- Self-concordant barriers
- Short / Long step path-following methods
- Barriers for non-symmetric cones
- Applications
- Control problems
- Analysis of dynamical systems
- Topology / Shape optimization
- Relaxations
- MaxCut (Goemans / Williamson)
- Stable set (Lovasz / Schrijver)
- Copositive programming relaxations
- Polynomial optimization
- Sums of squares relaxations
- Moment relaxations
Linear algebra: matrices, vector spaces, linear functions
Analysis: differentiability, gradients, convergence, continuity
Test
The course is composed of 18 hours lectures.
Evaluation : A two-hours written exam (E1) in session 1. For those who do not pass there will be another two-hours exam (E2) in session 2.
N1 = Exam1
N2 = Exam2
The exam is given in english only 
Calendar
The course exists in the following branches:
- Curriculum - Master in Applied Mathematics - Semester 9 (this course is given in english only
)
Additional Information
Course ID : WMM9AM16
Course language(s):
You can find this course among all other courses.
Bibliography
Aharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski. Robust Optimization. Princeton University Press, 2009.
Aharon Ben-Tal, Arkadi Nemirovski. Lectures on Modern Convex Optimization - Analysis, Algorithms, and Engineering Applications. Vol. 2 of MPS/SIAM Series on Optimization. SIAM, 2001.
Steven Boyd, Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
Jean-Bernard Lasserre. Moments, Positive Polynomials and their Applications. Vol. 1 of Imperial College Press Optimization Series. Imperial College Press, 2009.
Yurii Nesterov, Arkadi Nemirovski. Interior-Point Algorithms in Convex Programming. Vol. 13 of SIAM Stud. Appl. Math. SIAM, Philadelphia, 1994.