Lagrangian coordination for enhancing the convergence of analytical target cascading

Analytical target cascading is a hierarchical multilevel multidisciplinary design methodology. In analytical target cascading, top-level design targets (i.e., specifications) are propagated to lower-level design problems in a consistent and efficient manner. In this paper, a modified Lagrangian dual formulation and coordination for analytical target cascading are developed to enhance a formulation and coordination proposed earlier in the literature. The proposed approach guarantees all the properties established earlier and additionally offers new significant advantages. As established previously for the convex case, the proposed analytical target cascading coordination converges to a global optimal solution with corresponding optimal Lagrange multipliers in the dual space. The Lagrange multipliers can be viewed as the weights for deviations in analytical target cascading formulations. Thus the proposed coordination algorithm finds the optimal solution and the optimal weights for the deviation terms simultaneously. The enhancement allows for target cascading between levels, for the use of augmented Lagrangian to improve convergence of the coordination algorithm, and for prevention of unboundedness. A guideline to set the step size for subgradient optimization when solving the Lagrangian dual problem is also proposed.