Fall 2001 last updated 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 coneLP and examples, semidefinite, second order nonnegative 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 01 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, ConeLP 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 