Hierarchical overlapping coordination for large-scale optimization by decomposition

Decomposition of large engineering design problems into smaller design subproblems enhances robustness and speed of numerical solution algorithms. Design subproblems can be solved in parallel, using the optimization technique most suitable for the underlying subproblem. This also reflects the typical multidisciplinary nature of system design problems and allows better interpretation of results. Hierarchical overlapping coordination (HOC) simultaneously uses two or more problem decompositions, each of them associated with different partitions of the design variables and constraints. Coordination is achieved by the exchange of information between decompositions. We present the HOC algorithm and a sufficient condition for global convergence of the algorithm to the solution of a convex optimization problem. The convergence condition involves the rank of a matrix derived from the Jacobian of the constraints. Computational results obtained by applying the HOC algorithm to problems of various sizes are also presented.