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• W3104984361 abstract "We regard the real symplectic group $$Sp(2n,{{mathbb {R}}})$$ as a constraint submanifold of the $$2ntimes 2n$$ real matrices $${mathcal {M}}_{2n}({{mathbb {R}}})$$ endowed with the Euclidean (Frobenius) metric, respectively as a submanifold of the general linear group $$Gl(2n,{{mathbb {R}}})$$ endowed with the (left) invariant metric. For a cost function that defines an optimization problem on the real symplectic group we give a necessary and sufficient condition for critical points and we apply this condition to the particular case of a least square cost function. In order to characterize the critical points we give a formula for the Hessian of a cost function defined on the real symplectic group, with respect to both considered metrics. For a generalized Brockett cost function we present a necessary condition and a sufficient condition for local minimum. We construct a retraction map that allows us to detail the steepest descent and embedded Newton algorithms for solving an optimization problem on the real symplectic group." @default.
• W3104984361 created "2020-11-23" @default.
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• W3104984361 date "2020-01-27" @default.
• W3104984361 modified "2023-10-14" @default.
• W3104984361 title "Optimization on the real symplectic group" @default.
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• W3104984361 doi "https://doi.org/10.1007/s00605-020-01369-9" @default.
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