A Riemannian-steepest-descent approach for optimization on the real symplectic group

作者：Wang, Jing; Sun, Huafei^*; Fiori, Simone

来源：Mathematical Methods in the Applied Sciences, 2018, 41(11): 4273-4286.

DOI：10.1002/mma.4890

• extended Hamiltonian algorithm
• geodesic
• real symplectic group
• Riemannian-steepest-descent algorithm

In this paper, we first give the geodesic in closed form on the real symplectic group endowed with a Riemannian metric and then study a geodesic-based Riemannian-steepest-descent approach to compute the empirical average out of a set of symplectic matrices. The devised averaging algorithm is compared with the Euclidean gradient algorithm and the extended Hamiltonian algorithm. Simulation examples show that the convergence of the geodesic-based Riemannian-steepest-descent algorithm is the fastest among the 3 considered algorithms.

• 出版日期2018-7-30
• 单位北京理工大学