A Recurrent Neural Network Approach for Constrained Distributed Fuzzy Convex Optimization

This article investigates a class of constrained distributed fuzzy convex optimization problems, where the objective function is the sum of a set of local fuzzy convex objective functions, and the constraints include partial order relation and closed convex set constraints. In undirected connected node communication network, each node only knows its own objective function and constraints, and the local objective function and partial order relation functions may be nonsmooth. To solve this problem, a recurrent neural network approach based on differential inclusion framework is proposed. The network model is constructed with the help of the idea of penalty function, and the estimation of penalty parameters in advance is eliminated. Through theoretical analysis, it is proven that the state solution of the network enters the feasible region in finite time and does not escape again, and finally reaches consensus at an optimal solution of the distributed fuzzy optimization problem. Furthermore, the stability and global convergence of the network do not depend on the selection of the initial state. A numerical example and an intelligent ship output power optimization problem are given to illustrate the feasibility and effectiveness of the proposed approach.