Distributed Global Optimization for a Class of Nonconvex Optimization With Coupled Constraints
Distributed Global Optimization for a Class of Nonconvex Optimization With Coupled Constraints
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DOI：
10.1109/tac.2021.3115430
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发表时间：
2022-08
影响因子：
6.8
通讯作者：
Xiaoxing Ren;Dewei Li;Y. Xi;Haibin Shao
中科院分区：
文献类型：
--
作者：
Xiaoxing Ren;Dewei Li;Y. Xi;Haibin Shao
本文研究了静态网络上具有结构化非凸目标函数和耦合凸不等式约束的分布式非凸优化问题。提出了一种分布式连续时间原对偶算法来解决该问题。我们使用规范变换和拉格朗日乘子法将非凸优化问题重新表述为凸凹鞍点计算问题，随后采用投影原对偶次梯度法求解。提供了保证所提出算法生成的解的全局最优性的充分条件。给出了数值和应用示例来演示所提出的算法。
This article examines the distributed nonconvex optimization problem with structured nonconvex objective functions and coupled convex inequality constraints on static networks. A distributed continuous-time primal-dual algorithm is proposed to solve the problem. We use the canonical transformation and Lagrange multiplier method to reformulate the nonconvex optimization problem as a convex–concave saddle point computation problem, which is subsequently solved by employing the projected primal-dual subgradient method. Sufficient conditions that guarantee the global optimality of the solution generated by the proposed algorithm are provided. Numerical and application examples are presented to demonstrate the proposed algorithm.