  Despite significant progress on stability analysis of conventional multiagent
networked systems with weakly coupled state-network dynamics, most of the
existing results have shortcomings in addressing multiagent systems with highly
coupled state-network dynamics. Motivated by numerous applications of such
dynamics, in our previous work [1], we initiated a new direction for stability
analysis of such systems that uses a sequential optimization framework.
Building upon that, in this paper, we extend our results by providing another
angle on multiagent network dynamics from a duality perspective, which allows
us to view the network structure as dual variables of a constrained nonlinear
program. Leveraging that idea, we show that the evolution of the coupled
state-network multiagent dynamics can be viewed as iterates of a primal-dual
algorithm for a static constrained optimization/saddle-point problem. This view
bridges the Lyapunov stability of state-dependent network dynamics and
frequently used optimization techniques such as block coordinated descent,
mirror descent, the Newton method, and the subgradient method. As a result, we
develop a systematic framework for analyzing the Lyapunov stability of
state-dependent network dynamics using techniques from nonlinear optimization.
Finally, we support our theoretical results through numerical simulations from
social science.
