The recently proposed method of our research group named as directional Lyapunov exponents（DLEs） is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium point...The recently proposed method of our research group named as directional Lyapunov exponents（DLEs） is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium points. Finally, the impacts of the superlattice parameter changes on the characteristics of the output chaotic signal are analyzed. The experimental results show that parameter changes of the superlattice will affect the eigenstructure around the equilibrium points in the output phase space, and DLEs are sensitive to these changes.展开更多
The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The prox...The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.展开更多
文摘The recently proposed method of our research group named as directional Lyapunov exponents（DLEs） is presented. Then, DLEs are used to analyze the eigenstructure of the output phase space around the equilibrium points. Finally, the impacts of the superlattice parameter changes on the characteristics of the output chaotic signal are analyzed. The experimental results show that parameter changes of the superlattice will affect the eigenstructure around the equilibrium points in the output phase space, and DLEs are sensitive to these changes.
基金supported by the National Natural Science Foundation of China(11571074,61170308)the Natural Science Foundation of Fujian Province(2015J01010)the Major Science Foundation of Fujian Provincial Department of Education(JA14037)
文摘The alternating direction method of multipliers （ADMM for short） is efficient for linearly constrained convex optimization problem. The practicM computationM cost of ADMM depends on the sub-problem solvers. The proximal point algorithm is a common sub-problem-solver. However, the proximal parameter is sensitive in the proximM ADMM. In this paper, we propose a homotopy-based proximal linearized ADMM, in which a homotopy method is used to soNe the sub-problems at each iteration. Under some suitable conditions, the global convergence and the convergence rate of O（1/k） in the worst case of the proposed method are proven. Some preliminary numerical results indicate the validity of the proposed method.
