Fall 2001

last updated 01/03/02

Please Note that you should use the template file to prepare your notes in Latex. You may also use any of the notes prepared previously by other students.

Note 1 9/10/01

A general over view of semidefinite programming and related problems, examples

Note 2 9/17/01

Definition of Cones, and cone-LP and examples, semidefinite, second order non-negative and Moment cones

Note 3 9/24/01

Generalized Farkas Lemma, Duality theorem, contrast with Linear Programming

Note 4 10/1/01

Complementary slackness theorems, eigenvalue optimization

Note 5 10/8/01

Eigenvalue optimization, Lovasz theta function

Note 6 10/15/01

Sums of eigenvalues as semidefinite programs, sum of largest norms as SOCPs

Note 7 10/22/01

SDP relaxation of Independent set, clique and general 0-1 integer programming problems

Note 8 10/29/01

Introduction to logarithmic barrier function for LP, SDP and SOCP, Newton's method

Note 9 11/12/01

Finish up preliminary discussion of logarithmic barrier functions; Introduction to algebras, associative, power associative, and Jordan algebras; examples

Note 10 11/19/01

Minimum and characteristic polynomials, eigenvalues, trace, determinant, and introduction to the quadratic representation

Note 11 11/26/01

Properties of quadratic representation, Euclidean Jordan algebras, spectral decomposition, symmetric cones, Cone-LP over symmetric cones and the basic system of equations in Jordan algebraic terms

Note 12 12/3/01

Spectral decomposition in Euclidean Jordan Algebras, Cone of squares, relation to LP, SOCP, SDP

The entire notes plus the end of semester presentation of students can be found in

Lecture Notes