On the linear convergence of distributed Nash equilibrium seeking for multi-cluster games under partial-decision information

This paper considers the distributed strategy design for Nash equilibrium (NE) seeking in multi-cluster games under a partial-decision information scenario. In the considered game, there are multiple clusters and each cluster consists of a group of agents. A cluster is viewed as a virtual noncooperative player that aims to minimize its local payoff function and the agents in a cluster are the actual players that cooperate within the cluster to optimize the payoff function of the cluster through communication via a connected graph. In our setting, agents have only partial-decision information, that is, they only know local information and cannot have full access to opponents' decisions. To solve the NE seeking problem of this formulated game, a discrete-time distributed algorithm, called distributed gradient tracking algorithm (DGT), is devised based on the inter- and intra-communication of clusters. In the designed algorithm, each agent is equipped with strategy variables including its own strategy and estimates of other clusters' strategies. With the help of a weighted Fronbenius norm and a weighted Euclidean norm, theoretical analysis is presented to rigorously show the linear convergence of the algorithm. Finally, a numerical example is given to illustrate the proposed algorithm

Surface diffuseness correction in global mass formula

By taking into account the surface diffuseness correction for unstable nuclei, the accuracy of the macroscopic-microscopic mass formula is further improved. The rms deviation with respect to essentially all the available mass data falls to 298 keV, crossing the 0.3 MeV accuracy threshold for the first time within the mean-field framework. Considering the surface effect of the symmetry potential which plays an important role in the evolution of the "neutron skin" toward the "neutron halo" of nuclei approaching the neutron drip line, we obtain an optimal value of the symmetry energy coefficient J=30.16 MeV. With an accuracy of 258 keV for all the available neutron separation energies and of 237 keV for the alpha-decay Q-values of super-heavy nuclei, the proposed mass formula is particularly important not only for the reliable description of the r-process of nucleosynthesis but also for the study of the synthesis of super-heavy nuclei.Comment: 2 figures, 2 tables, to appear in Phys. Lett.