SEQUENTIALLY DECOMPOSED PROGRAMMING

Model-based decomposition is a powerful tool for breaking design probl ems into smaller subproblems, establishing hierarchical structure, and analyzing the interrelations in engineering design problems. However, the theoretical foundation for solving decomposed nonlinear optimizat ion problems requires further work. We show that the formulation of th e coordination problem is critical in quickly identifying the correct active constraints and that solving subproblems independently may hind er the local convergence of algorithms tailored to hierarchical coordi nation. Yet hierarchical decomposition algorithms can have excellent g lobal convergence properties and can be expected to exhibit superior i mprovement in the first few iterations when compared to the undecompos ed case. Based on these insights, a generic sequentially decomposed pr ogramming (SDP) algorithm is outlined. SDP has two phases: far from th e 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 ar e given.