A Distributed Penalty-Like Function Approach for the Nonconvex Constrained Optimization Problem

This letter addresses distributed nonconvex constrained optimization problems, where both the local cost function and the inequality constraint function are nonconvex. Firstly, the global nonlinear equality constraint is added to the global cost function via a penalty-like function method. Then, based on the consensus technique of multiagent systems, the global nonlinear equality constraint is estimated through a distributed nonlinear consensus scheme within a finite time. Secondly, the local inequality constraint is managed with an adaptive penalty factor. Thirdly, the optimal outcome is attained by employing the gradient of the augmented Lagrangian function. The stability analysis is performed using the Lyapunov theory. Lastly, a simulation case on the economic dispatch problem in smart grids is presented to clarify the developed theoretical result.