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Euclidean Jordan algebras and generalized
affine-scaling vector fields

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L. Faybusovich

We describe the phase portrait of generalized affine- scaling vector
fields for optimization problems involving symmetric cones. A Poisson
structure on the complexification of a real Euclidean Jordan algebra
is introduced. Nonconstrained affine-scaling vector fields
are proved to be Hamiltonian with respect to this
Poisson structure. Constained affine-scaling vector
fields are obtained as a symplectic reduction of
unconstrained ones. It is proved that constrained
affine-scaling vector fields are completely integrable Hamiltonian
vector fields and action-angle variables are
constructed for them.
Research report, University of Notre Dame, January, 1998

Contact: lfaybuso@toda.math.nd.edu