Symmetric Reduction and Hamilton-Jacobi Equation of Rigid Spacecraft with a Rotor

In this paper, we consider the rigid spacecraft with an internal rotor as a regular point reducible regular controlled Hamiltonian (RCH) system. In the cases of coincident and non-coincident centers of buoyancy and gravity, we give explicitly the motion equation and Hamilton-Jacobi equation of reduced spacecraft-rotor system on a symplectic leaf by calculation in detail, respectively, which show the effect on controls in regular symplectic reduction and Hamilton-Jacobi theory.Comment: 21 pages. Revised some printed wrongs in section 4. arXiv admin note: substantial text overlap with arXiv:1305.3457, arXiv:1303.5840, arXiv:1202.356

A Nonconvex Splitting Method for Symmetric Nonnegative Matrix Factorization: Convergence Analysis and Optimality

Symmetric nonnegative matrix factorization (SymNMF) has important applications in data analytics problems such as document clustering, community detection and image segmentation. In this paper, we propose a novel nonconvex variable splitting method for solving SymNMF. The proposed algorithm is guaranteed to converge to the set of Karush-Kuhn-Tucker (KKT) points of the nonconvex SymNMF problem. Furthermore, it achieves a global sublinear convergence rate. We also show that the algorithm can be efficiently implemented in parallel. Further, sufficient conditions are provided which guarantee the global and local optimality of the obtained solutions. Extensive numerical results performed on both synthetic and real data sets suggest that the proposed algorithm converges quickly to a local minimum solution.Comment: IEEE Transactions on Signal Processing (to appear