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KTH /
Teknikvetenskap
/
Matematik
/
Optimeringslära och systemteori
SF3810 Convexity and optimization in linear spaces, 7,5 hp, January-April
2012.
This course deals with
optimization theory in infinite
dimensional vector spaces.
It is one of the core courses in the doctoral program in Applied and
Computational Mathematics at KTH.
Lecturer and examiner:
Krister Svanberg ,
krille@math.kth.se ,
rum 3704, 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.
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.
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.
Examination:
Examination through home assignments during the course, and
a final oral exam.
Reading instructions and preliminary plan for the lectures.
Click here.
Time and place:
All lecture will be held in the seminar room 3721,
Lindstedtsvägen 25.
Lecture 1: Thursday, January 19, 13.15--15.00.
Lecture 2: Tuesday, January 24, 15.15--17.00.
Lecture 3: Tuesday, January 31, 15.15--17.00.
Lecture 4: Tuesday, February 7, 15.15--17.00.
Lecture 5: Tuesday, February 14, 15.15--17.00.
Lecture 6: Tuesday, February 21, 15.15--17.00.
There will be 14 or 15 lectures.
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