Once we obtain a convex problem for R s,n and since the optimization problem of R p,n is convex, the global problem can be handled by alternating optimization method [38].
Now, we can obtain a problem formulation in terms of the user powers only by replacing the following expression in (29): ∥ w k, n, s ∥ 2 = γ k, n, s 2 p k, n, s, (32).
Under some realistic assumptions on the data, we obtain a nonlinear homogenized problem with effective coefficients which are computed via a cell problem.
Clearly, if we allow few possible reactions and narrow parameter ranges we obtain a simpler identification problem, and if we allow many possible reactions and wide parameter ranges we obtain a more difficult problem.
With some simplifications, we obtain a convex optimization problem.
Then, by adopting SDP relaxation (SDR) technique [15], remove C8, we obtain a convex SDR problem.
As such, we obtain a conventional planning problem {D,I,G}.
For each realization of this parameter ξ ∈ U we obtain a single optimization problem.
Because of this, the EKF [3] cannot be applied easily and we obtain a challenging benchmark problem.
Since the objective function is linear, we obtain a convex optimization problem for which strong duality holds so that it can equivalently be solved in the dual domain.
