Course
Title: Optimization over Vector Spaces
This course module will cover the basic theory of
optimization over vector spaces and application of this theory to optimal
control problems. This module will be taught in about 5 weeks (about 15
lectures of 1 hour duration). The following topics will be covered:
1. Normed
Linear Spaces-Banach Spaces, Hilbert Spaces (Review)
2. Dual
Spaces-Linear Functionals, Hahn-Banach Theorem: (extension and geometric form)
3. Optimization
of Functionals: Gateaux and Frechet Differentials,
Euler Lagrange equations, Min-max theorem
4. Constrained
Optimization:
a. Lagrange
Multiplier theorems
b. Optimal
Control theory (Pontryagin’s maximum principle)
Text: David G Luenberger, “Optimization by Vector Space Methods,” 1969
John Wiley and Sons, New York.
Lecture Notes (Summer 2011)
1. Hahn Banach
Theorem: Extension Form
2. Hahn Banach
Theorem: Geometric Form