This article focuses on multiagent distributed-constrained optimization problems in a dynamic environment, in which a group of agents aims to cooperatively optimize a sum of time-changing local cost functions subject to time-varying coupled constraints. Both the local cost functions and constraint functions are unrevealed to an individual agent until an action is submitted. We first investigate a gradient-feedback scenario, where each agent can access both values and gradients of cost functions and constraint functions owned by itself at the chosen action. Then, we design a distributed primal-dual online learning algorithm and show that the proposed algorithm can achieve the sublinear bounds for both the regret and constraint violations. Furthermore, we extend the gradient-feedback algorithm to a gradient-free setup, where an individual agent has only attained the values of local cost functions and constraint functions at two queried points near the selected action. We develop a bandit version of the previous method and give the explicitly sublinear bounds on the expected regret and expected constraint violations. The results indicate that the bandit algorithm can achieve almost the same performance as the gradient-feedback algorithm under wild conditions. Finally, numerical simulations on an electric vehicle charging problem demonstrate the effectiveness of the proposed algorithms.

Increasing penetration of plug-in electric vehicles (PEVs) has a substantial impact on the operation of power distribution networks. Given the fast-growing load demands from PEVs and unmatched infrastructure investment in transformer and feeder capacity, the PEV charging is subjected to both spatially and temporally security constraints beyond which the network failure may occur. This paper proposes a game-theory-based distributed charging control method to coordinate large-scale PEVs without compromising the security of the distribution network. Under a noncooperative game framework, a price-driven charging model is designed to minimize the cost of each individual PEV customer while satisfying the network loading constraints. Then, a Newton-type method is developed to find a better Nash equilibrium of the game model at a superlinear convergence rate. Furthermore, an accelerated gradient method is proposed to tackle the subproblem for each user's best response. The update of the user's best response is implemented in a distributed way in order to protect user's privacy. The convergence rate of the proposed algorithms is rigorously proved. The effectiveness and efficiency of the proposed methods are tested on the IEEE 13-bus system.