Euclidean Jordan Algebras and Generalized Aane-scaling Vector Elds
نویسنده
چکیده
We describe the phase portrait of generalized aane-scaling vector elds for optimization problems involving symmetric cones. A Poisson structure on the complexiication of a real Jordan Euclidean algebra is introduced. Nonconstrained aane-scaling vector elds are proved to be Hamiltonian with respect to this Poisson structure. Constrained aane-scaling vector elds are obtained as a symplectic reduction of unconstrained ones. It is proved that constrained aane-scaling vector elds are completely integrable Hamiltonian vector elds and action-angle variables are constructed for them.
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