COCOA Talk: 99-02

Jordan Algebras and Optimization over Symmetric Cones

Speaker: Stefan H. Schmieta


Optimization over symmetric cones includes the well-studied cases
of linear and semi-definite programming as well as optimization
over the second-order cone (SOCP). We concentrate on SOCP, a
class of optimization problems that includes a wide variety of
application in finance and engineering.  

We develop primal-dual interior point methods for such problems
which are analogues of known algorithms for semi-definite
programming. We show that these algorithms can handle sparse 
constraints in a way similar to algorithms for linear programming
and thus are better suited for large-scale problems than their
semi-definite counterparts.

On a final note, we point out that, using Jordan algebra
techniques, we can extend our algorithms and their analysis to
all symmetric cones.

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