A power reformulation continuous-time algorithm for nonconvex distributed constrained optimization over multi-agent systems

A collective neurodynamic penalty approach to nonconvex distributed constrained optimization

A nonconvex distributed optimization problem involving nonconvex objective functions and inequality constraints within an undirected multi-agent network is considered. Each agent communicates with its neighbors while only obtaining its individual local information (i.e. its constraint and objective function information). To overcome the challenge caused by the nonconvexity of the objective function, a collective neurodynamic penalty approach in the framework of particle swarm optimization is proposed. The state solution convergence of every neurodynamic penalty approach is directed towards the critical point ensemble of the nonconvex distributed optimization problem. Furthermore, employing their individual neurodynamic models, each neural network conducts accurate local searches within constraints. Through the utilization of both locally best-known solution information and globally best-known solution information, along with the incremental enhancement of solution quality through iterations, the globally optimal solution for a nonconvex distributed optimization problem can be found. Simulations and an application are presented to demonstrate the effectiveness and feasibility.

Two-timescale projection neural networks in collaborative neurodynamic approaches to global optimization and distributed optimization

In this paper, we propose a two-timescale projection neural network (PNN) for solving optimization problems with nonconvex functions. We prove the convergence of the PNN with sufficiently different timescales to a local optimal solution. We develop a collaborative neurodynamic approach with multiple such PNNs to search for global optimal solutions. In addition, we develop a collaborative neurodynamic approach with multiple PNNs connected via a directed graph for distributed global optimization. We elaborate on four numerical examples to illustrate the characteristics of the approaches.