Abstract
This paper is concerned with a distributed optimization problem with inequality constraint over a multiagent network. The objective function is the sum of multiple local convex functions, which can be nonsmooth. Based on graph theory and nonsmooth analysis, we propose a neural network with a time-varying auxiliary function. The boundedness of the state solution is demonstrated by using the properties of the auxiliary function. Moreover, it is proved that the designed neural network with any initial conditions reaches a consensus and converges to the global optimal solution. Finally, a numerical simulation is discussed to verify the theoretical results.
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