Fast Inexact Decomposition Algorithms For Large-Scale Separable Convex Optimization

In this paper we propose a new inexact dual decomposition algorithm for solving separable convex optimization problems. This algorithm is a combination of three techniques: dual Lagrangian decomposition, smoothing and excessive gap. The algorithm requires only one primal step and two dual steps at each iteration and allows one to solve the subproblem of each component inexactly and in parallel. Moreover, the algorithmic parameters are updated automatically without any tuning strategy as in augmented Lagrangian approaches. We analyze the convergence of the algorithm and estimate its $O(\frac{1}{\varepsilon})$ worst-case complexity. Numerical examples are implemented to verify the theoretical results.