id: 05998020
dt: j
an: 05998020
au: Fiori, Simone
ti: Solving minimal-distance problems over the manifold of real-symplectic
    matrices.
so: SIAM J. Matrix Anal. Appl. 32, No. 3, 938-968 (2011).
py: 2011
pu: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
la: EN
cc: 
ut: group of real-symplectic matrices; pseudo-Riemannian geometry;
    gradient-based optimization on manifolds; geodesic-stepping method;
    numerical examples; minimal-distance problem; convergence
ci: 
li: doi:10.1137/100817115
ab: The author discusses a minimal-distance problem formulated over the
    manifold of real-symplectic matrices. The real-symplectic group is
    regarded as a pseudo-Riemannian manifold, and a metric is chosen that
    affords the computation of closed forms of geodesic arcs. Survey
    results on the computation of geodesic arcs and of the
    pseudo-Riemannian gradient of a regular function on the manifold of
    real-symplectic matrices are presented. The author discusses the
    difficulties encountered when trying to extend the Riemannian
    optimization setting to a general manifold, and the selection of a
    stepsize schedule with the stopping criteria on the convergence and the
    computational issues related to the optimization method. The numerical
    behavior of the proposed minimal-distance algorithms is illustrated by
    some numerical experimental results.
rv: Hang Lau (Montréal)