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 video lectures and homeworks)
• Linear Programming
• 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
• Dynamic Programming

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).
• Linear and Nonlinear Programming by D. G. Luenberger (recommended)
• Principles of Mathematical Analysis, W. Rudin (recommended).
• Convex Optimization, Boyd and Vandenberghe (recommended)
• Dynamic Programming and Optimal Control by D. P. Bertsekas (recommended)

Course Notes:

linearAlgebraNotes.pdf (not covered in class)

Linear Programming

Hilbert Space Optimization

Time
4-5:15pm T,Th,

Place
Keller 5-120

Office Hours
T: 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. Linear Algebra Homework