A Newton consensus method for distributed optimization

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. Copyright (C) 2020 The Authors.