Distributed Method of Multiplier for Coupled Lagrangian Problems: A Control Approach
Abhishek Rawat, Nicola Elia · 2018
In this paper, we propose a method for solving the distributed optimization problem in which the objective function is the sum of separable convex functions with linear constraints. In our approach, the primal variable is partially updated to make the Method of Multiplier algorithm distributed which is based on the suitable scaling of constraint matrix. The algorithm is then viewed as a dynamical system the convergence analysis of which is done using the passivity concepts of nonlinear control theory. The convexity of the function is related to the passivity of the non-linear functions which is in feedback with the positive real linear system.