H. Park et al., Convergence criteria for hierarchical overlapping coordination of linearlyconstrained convex design problems, COMPUT OP A, 18(3), 2001, pp. 273-293
Decomposition of multidisciplinary engineering system design problems into
smaller subproblems is desirable because it enhances robustness and underst
anding of the numerical results. Moreover, subproblems can be solved in par
allel using the optimization technique most suitable for the underlying mat
hematical form of the subproblem. Hierarchical overlapping coordination (HO
C) is an interesting strategy for solving decomposed problems. It simultane
ously uses two or more design problem decompositions, each of them associat
ed with different partitions of the design variables and constraints. Coord
ination is achieved by the exchange of information between decompositions.
This article presents the HOC algorithm and several new sufficient conditio
ns for convergence of the algorithm to the optimum in the case of convex pr
oblems with linear constraints. One of these equivalent conditions involves
the rank of the constraint matrix that is computationally efficient to ver
ify. Computational results obtained by applying the HOC algorithm to quadra
tic programming problems of various sizes are included for illustration.