EFIX: Exact fixed point methods for distributed optimization

Abstract We consider strongly convex distributed consensus optimization over connected networks. EFIX, the proposed method, is derived using quadratic penalty approach. In more detail, we use standard reformulation—transforming original problem into a constrained in higher dimensional space—to define sequence of suitable subproblems with increasing parameters. For objectives, corresponding consists subproblems. generic case, objective function approximated model and hence resulting again quadratic. EFIX then by solving each via fixed point (R)-linear solver, e.g., Jacobi Over-Relaxation method. The exact convergence proved as well worst case complexity order $${{\mathcal {O}}}(\epsilon ^{-1})$$ O ( ϵ - 1 ) for case. functions, result methods obtained. Numerical results indicate that method highly competitive state-of-the-art first methods, requires smaller computational communication effort, robust to choice algorithm