Augmented Lagrangian coordination for distributed optimal design in MDO

Quite a number of coordination methods have been proposed for the distributed optimal design of large-scale systems consisting of a number of interacting subsystems. Several coordination methods are known to have numerical convergence difficulties that can be explained theoretically. The methods for which convergence proofs are available have mostly been developed for so called quasi-separable problems (i.e. problems with individual subsystems coupled only through a set of linking variables, not through constraints and/or objectives). In this paper we present a new coordination approach for MDO problems with linking variables as well as coupling objectives and constraints. Two formulation variants are presented offering a large degree of freedom in tailoring the coordination algorithm to the design problem at hand. The first, centralized variant introduces a master problem to coordinate coupling of the subsystems. The second, distributed variant coordinates coupling directly between subsystems. Our coordination approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The proposed coordination algorithms can be shown to converge to Karush-Kuhn-Tucker (KKT) points of the original problem by using existing convergence results. We illustrate the flexibility of the proposed approach by showing that the Analytical Target Cascading method of [18] and theaugmented Lagrangian method for quasi-separable problems of [20] are subclasses of the proposed formulations.