Primal Resource-Directive Approaches for Optimizing Nonlinear Decomposable Systems

This study presents some new results on three primal-feasible computational approaches for optimizing a system composed of interrelated subsystems. The general structure treated is the same as the principal one of the classic paper by Dantzig and Wolfe, except that convex nonlinearities are permitted, provided that the overall criterion function and coupling constraints are separable by subsystem. Each approach decentralizes the optimization by iteratively allocating system resources to the subsystems, with each subsystem computing its own optimal utilization of the given resources at each iteration. The chief obstacle to directing the resource allocation centrally toward an overall optimum is that the optimal response of each subsystem, as a function of its allowed resources, is not available explicitly. All three procedures therefore approximate or generate the optimal response functions “as needed.”