Sequentially decomposed programming

Model-based decomposition is a powerful tool for breaking design problems into smaller subproblems, establishing hierarchical structure, and analyzing the interrelations in engineering design problems. However, the theoretical foundation for solving decomposed nonlinear optimization problems requires further work. We show that the formulation of the coordination problem is critical in quickly identifying the correct active constraints and that solving subproblems independently may hinder the local convergence of algorithms tailored to hierarchical coordination. Yet hierarchical decomposition algorithms can have excellent global convergence properties and can be expected to exhibit superior improvement in the first few iterations when compared to the undecomposed case. Based on these insights, a generic sequentially decomposed programming (SDP) algorithm is outlined. SDP has two phases: far from the solution (first phase) decomposition is used; close to the solution (second phase) subproblems are not solved separately. The generic SDP is applied to sequential quadratic programming (SQP) to define an SDP-SQP implementation. A global convergence proof and a simple example are given.