This manuscript proposes a distributed Newton seeking for the solution of distributed optimization problems with locally measured but unknown cost functions. The approach implements a Newton step for both the primal and dual problems that can be implemented in a completely decentralized fashion. Unlike existing techniques, no exchange of derivative information between agents is required. In addition, no explicit inversion of the Hessian information is required to generate the required Newton step. The local gradients and Hessians are estimated using a perturbation based extremum seeking control technique. A simulation study demonstrates the effectiveness of the technique.

该手稿提出了一种分布式牛顿算法，以解决具有局部测量但未知成本函数的分布式优化问题。该方法对原始问题和对偶问题都实施了牛顿步骤，可以完全分散地实施。与现有技术不同，无需在代理之间交换派生信息。另外，生成所需的牛顿步数不需要对Hessian信息进行显式反转。使用基于摄动的极值搜索控制技术估计局部梯度和Hessian。仿真研究证明了该技术的有效性。