MATE 5049 Calculus of variations
- Where and when
- MJ 9:00--10:15, in M-118.
Topics
- Introduction
- Vector space: examples, subspaces, affine varieties, convexity
and cones.
- Normed linear space: definition, open and closed sets,
convergence, continuity, Banach space, extreme values and
compactness.
- Hilbert space: pre-Hilbert space, approximation, minimum norm
problems.
- Dual spaces: linear functionals, dual, analytic and geometric
forms of the Hahn-Banach theorem.
- Linear operators and adjoints: fundamentals, invertibility,
adjointness and duality, optimisation in Hilbert space.
- Optimisation of functionals, local theory: Gateaux and Frechet
differentials, extrema, Euler-Lagrange equations, constrained
problems.
- Optimisation of functionals, global theory: convex and concave
functionals, dual optimisation problems, min-max theorem of
Game theory.
- Other topics, as time permits.
- Text
- "Optimization by vector space methods" by David Luenberger,
John Wiley, 1969.
- Grading policy
-
| homework |
30% |
| project or presentation |
15% |
| mid-term exam |
25% |
| final exam |
30% |
- Homework updated Mar 10.
Last modified: Tue Mar 10 00:12:01 AST 2009