An augmented Lagrangian coordination method for distributed optimal design in MDO: Part I formulation and algorithms

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 shared variables, not through constraints and/or objectives). In this paper we present a new coordination method for MDO problems with coupling variables as well as coupling objectives and constraints. Our approach employs an augmented Lagrangian penalty relaxation in combination with a block coordinate descent method. The coordination method can be shown to converge to KKT points of the original problem by using existing convergence results. 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. In a sequel paper we demonstrate the flexibility of the formulations, and investigate the numerical behavior of the proposed method.