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KTH / Teknikvetenskap / Matematik / Optimeringslära och systemteori

SF3810 Convexity and optimization in linear spaces, 7,5 hp, Sep-Dec 2017.

This course deals with optimization theory in infinite dimensional vector spaces. It is one of the core courses in the doctoral program Applied and Computational Mathematics at KTH.

Lecturer and examiner:

Krister Svanberg , , room 3531, Lindstedtsv 25, tfn 790 7137

Main content:

Basic theory for normed linear spaces.
Minimum norm problems in Hilbert and Banach spaces.
Convex sets and separating hyperplanes.
Adjoints and pseudoinverse operators.
Convex functionals and their corresponding conjugate functionals.
Fenchel duality.
Global theory of constrained convex optimization.
Lagrange multipliers and dual problems.
Gateaux and Frechet differentials.
Local theory of constrained optimization.
Kuhn-Tucker optimality conditions in Banach spaces.


Mathematics corresponding approximately to a Master of science in engineering physics, including a basic course in optimization.


David G Luenberger: Optimization by vector space methods,
John Wiley \& Sons. Paperback, ISBN: 0-471-18117-X.


Mandatory homework assignments and a mandatory oral exam.
There will be in total six collections of homeworks, one collection every second week.

Time and place for the lectures:

The address to the Seminar room F11 is Lindstedtsvägen 22.

Lecture 1: Wednesday, Sep 6, 15.15--17.00, room F11.
Lecture 2: Wednesday, Sep 13, 15.15--17.00, room F11.
Lecture 3: Wednesday, Sep 20, 15.15--17.00, room F11.
Lecture 4: Wednesday, Sep 27, 15.15--17.00, room F11.
Lecture 5: Wednesday, Oct 4, 15.15--17.00, room F11.
Lecture 6: Wednesday, Oct 11, 15.15--17.00, room F11.
Lecture 7: Wednesday, Oct 18, 15.15--17.00, room F11.
Lecture 8: Wednesday, Oct 25, 15.15--17.00, room 3733, Math department, floor 7.
Lecture 9: Wednesday, Nov 1, 15.15--17.00, room F11.
Lecture 10: Wednesday, Nov 8, 15.15--17.00, room F11.
Lecture 11: Wednesday, Nov 15, 15.15--17.00, room F11.
Lecture 12: Wednesday, Nov 22, 15.15--17.00, room F11.
Lecture 13: Wednesday, Nov 29, 15.15--17.00, room F11.

There will be on average one lecture per week during 13 weeks. Some weeks there might be two lecture, and some weeks none, but most weeks there will be one lecture.