EE8950: Vector Space Optimization

Professor Salapaka
5-161, EECS Bldg., 200 Union St. SE
Email: murtis@umn.edu
Ph: 1-612-625-7811
URL: http://www.ece.umn.edu/users/murtis/

Course Outline
This a course on Vector Space Optimization where the underlying space will retain the geometric structure of Euclidean spaces but will be general enough to be applicable to infinite dimensional spaces.  Its expected that students have a reasonable background in matrices and familiarity with rudimentary analysis. Course notes will be provided. The material will borrow from the Optimization by Vector Space Methods by Luenberger with the material developed in a Hilbert Space setting.

Topics

• Linear Algebra review (mostly a set of homeworks)
• Linear  Spaces(Vector Spaces), norms, completeness
• Hilbert Spaces (projection theorem, complete orthonormal sequences, Minimum norm problems)
• Estimation
• Convex optimization (distance to a convex set, Separating hyperplanes, sensitivity analysis, KKT)
• Optimization of functionals (Gateaux and Frechet derivatives, Euler-lagrange equations, problems with constraints,calculus of variatioins)
• Pontryagins Maximum principle

Text

• Optimization by vector space methods, Luenberger (recommended).

The following references will be helpful

• Matrix theory, James M. Ortega, Plenum press. (recommended)
• Matrix Analysis, Horn and Johnson (recommended).
• Principles of Mathematical Analysis, W. Rudin (recommended).
• Convex Optimization, Boyd and Vandenberghe (recommended)

Course Notes:

Linear Algebra Preliminaries (not covered in class)

Hilbert Space Optimization

Lectures

Lecture 3, Lecture 4, Lecture 5, Lecture 6, Lecture 7, Lecture 8,

Lecture 9,  Lecture 10,  Lecture 11, Lecture 12, Lecture 13, Lecture 14

Lecture 15 Lecture 16 Lecture 17 Lecture 18 Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26

Lecture27 Lecture28

Time
12:45-2pm

Place
CivE213

Office Hours
Th: 3-4pm and by appointment

Tentative Grading Policy
The course will rely heavily on an extensive set of homeworks. 50% Homeworks, 25% Midterms, 25% Finals.

Handouts:

Homeworks :

1. Homework 1
2. Homework 2
3. Homework3
4. Homework 4
5. Homework 5