Continuous-Time Algorithm Based on Finite-Time Consensus for Distributed Constrained Convex Optimization

• 成果类型: Article
• 署名作者: Liu, Hongzhe; Zheng, Wei Xing; Yu, Wenwu
• 署名单位: Western Sydney University; Southeast University - China; Southeast University - China
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3079192
• 发表日期: 2022
• 页码: 2552-2559
• 关键词: Optimization; Convex functions; Distributed algorithms; CONVERGENCE; linear programming; Multi-agent systems; graph theory; distributed optimization; finite-time consensus; general constraints; primal-dual algorithm

摘要

This article studies the convex optimization problem with general constraints, where its global objective function is composed of the sum of local objective functions. The objective is to design a distributed algorithm to cooperatively resolve the optimization problem under the condition that only the information of each node's own local cost function and its neighbors' states can be obtained. To this end, the optimality condition of the researched optimization problem is developed in terms of the saddle point theory. On this basis, the corresponding continuous-time primal-dual algorithm is constructed for the considered constrained convex optimization problem under time-varying undirected and connected graphs. In the case that the parameters involved in the proposed algorithm satisfy certain inequality, the states of all nodes will reach consensus in finite time. Meanwhile, the average state is globally convergent to the optimal solution of the considered optimization problem under some mild and standard assumptions.