SF3810

FSF3810 Convexity and optimization in linear spaces, 7,5 hp, Spring 2025.

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.

Schedule:

First class January 28, 10.15-12.00.
Schedule: Tuesdays: 10.15-12.00. (No classes 18/2, 1/4, 22/4)

Location: 3721, Lindstedtsvägen 25.

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 or applied mathematics, 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 1