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FSF3810 Convexity and optimization in linear spaces, 7,5 hp, Jan-May 2020.

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:

Johan Karlsson, email: johan.karlsson _at_ math.kth.se, room 3550, Lindstedtsv 25, tfn 790 8440

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.

Prerequisites:

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

Literature:

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

Reading instructions and preliminary plan for the lectures.

Preliminary course plan.

Examination:

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

Homework 6

Time and place for the lectures:

The address to the Seminar room F11 is Lindstedtsvägen 22.
The address to the Seminar room 3418 is Lindstedtsvägen 25.

Lecture 1: Wednesday, Jan 22, 13.15--15.00, room 3418.
Lecture 2: Wednesday, Jan 29, 13.15--15.00, room F11.
Lecture 3: Wednesday, Feb 5, 13.15--15.00, room 3418.
Lecture 4: Wednesday, Feb 12, 13.15--15.00, room F11.
Lecture 5: Wednesday, Feb 19, 13.15--15.00, room F11.
Lecture 6: Wednesday, Feb 26, 13.15--15.00, room F11.
Lecture 7: Wednesday, Mar 4, 13.15--15.00, room F11.
Lecture 8: Wednesday, Mar 11, 13.15--15.00, room F11.
Lecture 9: Wednesday, Mar 18, 13.15--15.00, room F11. (Lecture cancelled, see lecture notes.)
Lecture 10: Wednesday, Mar 25, 13.15--15.00, room F11. (Lecture cancelled, see lecture notes.)
Lecture 11: Wednesday, Apr 22, 13.15--15.00.
Lecture 12: Wednesday, Apr 29, 13.15--15.00.
Lecture 13: Wednesday, May 6, 13.15--15.00.
Lecture 14: Wednesday, May 13, 13.15--15.00.
Lecture 15: Wednesday, May 20, 13.15--15.00.


https://www.math.kth.se/optsyst/forskning/forskarutbildning/SF3810/