Distributed Adaptive Event-Triggered Algorithms for Nonsmooth Resource Allocation Optimization Over Switching Topologies

In this article, a distributed optimization algorithm is proposed for solving a distributed resource allocation problem (DRAP) with general inequality and heterogeneous coupled equality constraints. The communication topologies herein are considered to be jointly connected and directed interacted. To deal with the effects of inequality constraints, an adaptive item of updating penalty gain on-line is introduced in algorithmic design, which enforces the state enter to the constraint sets dynamically. Further, with the aid of Lyapunov method, the convergence to global optimal solution of nonsmooth DRAP is obtained. To effectively alleviate the communication burden caused by frequent interactions, an event-triggered mechanism is proposed to drive the agents with free-initial state, while also ensuring the exclusion of Zeno behavior. Compared with existing algorithms for DRAP, the time-varying auxiliary function designed in distributed algorithms herein avoids the preemptive estimation of global parameters that may cause the failure of the distributed framework, including the global Lipschitz coefficients of objective functions and the eigenvalues of full Laplacian matrix. Finally, numerical simulations and application of economic dispatch in smart grid illustrate the validity of designed algorithm.