- Basic theory for normed linear spaces.
- Minimum norm problems in Hilbert and Banach spaces.
- Convex sets and separating hyperplanes.
- Adjoints and pseudoinverse operators.
- Gateaux and Frechet differentials.
- Convex functionals and their corresponding conjugate functionals.
- Fenchel duality.
- Global theory of constrained convex optimization.
- Lagrange multipliers and dual problems.
- Local theory of constrained optimization.
- Kuhn-Tucker optimality conditions in Banach spaces.
FSF3810 Convexity and Optimization in Linear Spaces 7.5 credits
Information per course offering
Course offerings are missing for current or upcoming semesters.
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3810 (Spring 2019–)Headings with content from the Course syllabus FSF3810 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
That the student should obtain a deep understanding of the basic concepts and mathematical theory for optimization in infinite-dimensional vector spaces.
After completed course, the student should be able to
- demonstrate a good overview of the various subjects in the course, and how they connect to each other,
- explain and discuss the main concepts and theoretical results in the course,
- rigorously prove some selected main theorems,
- use the concepts and theoreticals results from the course to solve various application problems analytically or (when needed) numerically.
Literature and preparations
Specific prerequisites
A Master degree including at least 30 university credits (hp) in in Mathematics (Calculus, Linear algebra, Differential equations and transform method), and further at least 6 hp in Mathematical Statistics, 6 hp in Numerical analysis and 6 hp in Optimization.
Suitable prerequisity is a Master degree in Applied and Computational Mathematics, including some basic course in optimization, or similar knowledge.
Equipment
No information inserted
Literature
David G Luenberger: Optimization by vector space methods, John Wiley & Sons. Paperback, ISBN: 0-471-18117-X.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
P, F
Examination
- INL1 - Assignment, 3.5 credits, grading scale: P, F
- TENM - Oral exam, 4.0 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
Homework assignments and a final oral exam.
Other requirements for final grade
Homework assignments and a final oral exam.
Opportunity to complete the requirements via supplementary examination
No information inserted
Opportunity to raise an approved grade via renewed examination
No information inserted
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
This course does not belong to any Main field of study.
Education cycle
Third cycle
Add-on studies
No information inserted
Contact
Johan Karlsson (johan.karlsson@math.kth.se)