The differentiability of a norm of a Banach space may be characterized by its unit sphere.This paper generalizes these geometric conditions of norm’s differentiability to the case of a regular locally Lipschitz funct...The differentiability of a norm of a Banach space may be characterized by its unit sphere.This paper generalizes these geometric conditions of norm’s differentiability to the case of a regular locally Lipschitz function.展开更多
Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈h(...Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈h(x) + H(x), where h : X → Y is a smooth function on Ω ⊆X and H : X ⇉2<sup>Y</sup> is a set valued mapping with closed graph. When H is metrically regular and under some sufficient conditions, we analyze both semi-local and local convergence of the modified G-PPA. Moreover, the convergence results of the modified G-PPA are justified by presenting a numerical example.展开更多
We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of nu...We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.展开更多
基金Supported by the National Natural Science Foundation of China
文摘The differentiability of a norm of a Banach space may be characterized by its unit sphere.This paper generalizes these geometric conditions of norm’s differentiability to the case of a regular locally Lipschitz function.
文摘Consider X and Y are two real or complex Banach spaces. We introduce and study a modified Gauss-type proximal point algorithm (in short modified G-PPA) for solving the generalized equations of the form 0 ∈h(x) + H(x), where h : X → Y is a smooth function on Ω ⊆X and H : X ⇉2<sup>Y</sup> is a set valued mapping with closed graph. When H is metrically regular and under some sufficient conditions, we analyze both semi-local and local convergence of the modified G-PPA. Moreover, the convergence results of the modified G-PPA are justified by presenting a numerical example.
基金Supported by National Natural Science Foundation under Grant No.11002073the Fundamental Research Funds for the Central Universities under Grant No.2011RC0702
文摘We investigate the synchronization ability of four types of regular coupled networks. By introducing the proper error variables and Lyapunov functions, we turn the stability of synchronization manifold into that of null solution of error equations, further, into the negative definiteness of some symmetric matrices, thus we get the sufficient synchronization stability conditions. To test the valid of the results, we take the Chua's circuit as an example. Although the theoretical synchronization thresholds appear to be very conservative, they provide new insights about the influence of topology and scale of networks on synchronization, and that the theoretical results and our numerical simulations are consistent.
