The paper presents an effective coordination scheme for a distributed optimization based on dual decomposition. The targeted class of optimization problems are strictly convex quadratic functions with linear constraints, where the dual function with coupling equality constraints in Lagrangian is continuous piecewise quadratic. The coordination is based on multi-parametric programming - the subproblem solvers return their solution on a polyhedron around a given Lagrange multiplier value. Centralized coordinator constructs the gradient and Hessian of a dual function and reaches exact consensus in a finite number of iterations, while only some subproblems are queried for a new solution in each iteration. The algorithm is applied to the distributed model predictive control. The efficiency, in terms of optimization time and the number of iterations, is demonstrated on the distributed model predictive control of the Barcelona water distribution network.
['Pavel Trnka', 'Vladimir Havlena', 'Jaroslav Pekar']
Distributed MPC with parametric coordination