Distributed Online Optimization with Coupled Inequality Constraints over Unbalanced Directed Networks

This paper studies a distributed online convex optimization problem, where agents in an unbalanced network cooperatively minimize the sum of their time-varying local cost functions subject to a coupled inequality constraint. To solve this problem, we propose a distributed dual subgradient tracking algorithm, called DUST, which attempts to optimize a dual objective by means of tracking the primal constraint violations and integrating dual subgradient and push sum techniques. Different from most existing works, we allow the underlying network to be unbalanced with a column stochastic mixing matrix. We show that DUST achieves sublinear dynamic regret and constraint violations, provided that the accumulated variation of the optimal sequence grows sublinearly. If the standard Slater's condition is additionally imposed, DUST acquires a smaller constraint violation bound than the alternative existing methods applicable to unbalanced networks. Simulations on a plug-in electric vehicle charging problem demonstrate the superior convergence of DUST

Distributed optimization for multi-agent system over unbalanced graphs with linear convergence rate

summary:Distributed optimization over unbalanced graphs is an important problem in multi-agent systems. Most of literatures, by introducing some auxiliary variables, utilize the Push-Sum scheme to handle the widespread unbalance graph with row or column stochastic matrix only. But the introduced auxiliary dynamics bring more calculation and communication tasks. In this paper, based on the in-degree and out-degree information of each agent, we propose an innovative distributed optimization algorithm to reduce the calculation and communication complexity of the conventional Push-Sum scheme. Furthermore, with the aid of small gain theory, we prove the linear convergence rate of the proposed algorithm

Distributed robust optimization for multi-agent systems with guaranteed finite-time convergence

A novel distributed algorithm is proposed for finite-time converging to a feasible consensus solution satisfying global optimality to a certain accuracy of the distributed robust convex optimization problem (DRCO) subject to bounded uncertainty under a uniformly strongly connected network. Firstly, a distributed lower bounding procedure is developed, which is based on an outer iterative approximation of the DRCO through the discretization of the compact uncertainty set into a finite number of points. Secondly, a distributed upper bounding procedure is proposed, which is based on iteratively approximating the DRCO by restricting the constraints right-hand side with a proper positive parameter and enforcing the compact uncertainty set at finitely many points. The lower and upper bounds of the global optimal objective for the DRCO are obtained from these two procedures. Thirdly, two distributed termination methods are proposed to make all agents stop updating simultaneously by exploring whether the gap between the upper and the lower bounds reaches a certain accuracy. Fourthly, it is proved that all the agents finite-time converge to a feasible consensus solution that satisfies global optimality within a certain accuracy. Finally, a numerical case study is included to illustrate the effectiveness of the distributed algorithm.Comment: Submitted for publication in Automatic