Analytical Target Cascading is a method for design optimizationof hierarchical multilevel systems. A quadratic penaltyrelaxation of the system consistency constraints is used to arriveat a decomposition with feasible subproblems. A typicalnested solution strategy consists of inner and outer loops. Inthe inner loop the coupled subproblems are solved iterativelywith fixed penalty weights. After convergence of the innerloop the outer loop updates the penalty weights. The articlepresents an augmented Lagrangian relaxation that reducesthe computational cost associated with ill-conditioning ofsubproblems in the inner loop. The alternating directionsmethod of multipliers is used to update penalty parametersafter a single inner loop iteration, so that subproblems needto be solved only once. Experiments with four examplesshow that computational costs are decreased by orders ofmagnitude ranging between ten and one thousand.