Time-varying distributed optimization problem with inequality constraints

Abstract

This paper discusses a distributed time-varying convex optimization problem that agents have different Hessian matrices with inequality constraints. The objective is to minimize the sum of local time-varying objective functions of agents constrained by time-varying inequalities. Under the condition of undirected connected graph, a distributed continuous time consistency algorithm is designed based on average consensus estimator, sign function and log-barrier penalty function. The main idea of the algorithm proposed in this paper is to use the estimator to estimate the global information, make the state of agents reach consensus and achieve gradient descent to track the optimal solution. Theoretical findings show that all agents can reach an agreement, the proposed algorithm can track the optimal solution of the time-varying optimization problem. The effectiveness of the theoretical results is verified through a numerical examples.