Distributed robust optimization with coupled constraints via Tseng’s splitting method

Abstract

We consider distributed robust convex optimization with both local and coupled constraints, where coefficients with respect to local constraints are uncertain in polyhedral sets. We derive an equivalent optimization model with extended decision variables and finite constraints, and characterize its optimality condition. Also, we transform the problem as finding zeros of an operator and reveal the monotonicity of the underlying operator. By employing Tseng’s operator splitting method, we design a distributed algorithm to solve the considered robust optimization problem with guaranteed convergence, and also illustrate the efficiency in numerical simulations.