Sequentially decomposed programming
Sigurd A. Nelson, Panos Y. Papalambros · AIAA Journal · 1997
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 problems is not yet well established.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.Conversely, it is believed that hierarchical decomposition algorithms have excellent global convergence properties and usually exhibit superior improvement in the first few iterations when compared to the undecomposed case.Based on insights given in the paper, we outline a Sequentially Decomposed Programming (SDP) algorithm.SDP has two phases: when far from the solution, the first phase is enacted and decomposition is used; when close to the solution, the second phase is underway and decomposition is not used.The principles defining SDP are applied to Sequential Quadratic Programming (SQP) to define an SDP-SQP implementation.A global convergence proof and a simple example are given.