Lagrangian coordination and analytical target cascading: Solving ATC-decomposed problems with Lagrangian duality

Lagrangian duality is a powerful tool for dealing with large mathematical programs which require decomposition. We consider a large-scale convex nonlinear program that is decomposed according to the scheme of analytical target cascading and propose a Lagrangian duality-based coordination in which solutions of resulting subproblems converge to a solution of the original problem. We present a subgradient algorithm to achieve said solution, demonstrate with an example, and conclude with an extension to multiple level problems with multiple subsystems on each level.