Hierarchical overlapping coordination for large-scale optimization by decomposition

Decomposition of large engineering design problems into smaller design subp roblems enhances robustness and speed of numerical solution algorithms. Des ign subproblems can be solved in parallel, using the optimization technique most suitable for the underlying subproblem. This also reflects the typica l multidisciplinary nature of system design problems and allows better inte rpretation of results. Hierarchical overlapping coordination (HOC) simultan eously uses two or more problem decompositions, each of them associated wit h different partitions of the design variables and constraints. Coordinatio n is achieved by the exchange of information between decompositions. We pre sent the HOC algorithm and a sufficient condition for global convergence of the algorithm to the solution of a convex optimization problem. The conver gence condition involves the rank of a matrix derived from the Jacobian of the constraints. Computational results obtained by applying the ROC algorit hm to problems of various sizes are also presented.