A trace-penalty minimization converts the symplectic eigenvalue problem into unconstrained optimization whose stationary points match the original solutions, with a gradient algorithm that is faster than Riemannian methods on tested matrices.
Brockett cost function for symplectic eigenvalues
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Exact Quadratic Penalty Function for Symplectic Eigenvalue Problem
A trace-penalty minimization converts the symplectic eigenvalue problem into unconstrained optimization whose stationary points match the original solutions, with a gradient algorithm that is faster than Riemannian methods on tested matrices.