Primal Resource-Directive Approaches for Optimizing Nonlinear Decomposable Systems.

The optimization of large systems comprised of interrelated subsystems is considered. Three different methods are presented for decentralizing the optimization by partitioning into subsystems and iteratively allocating resources to the subsystems, followed by a coordination procedure. The Tangential Approximation method builds up a piecewise-linear approximation to the optimal response functions based on the optimal multipliers that become available at each iteration. These multipliers are also used by the Large-Step Subgradient approach, which extends a typical large-step gradient method to cope with the nondifferentiability of the response function. An explicit linear program is derived for finding the feasible direction yielding the greatest rate of increase in the maximand. The Piecewise approach exploits the relative simplicity in the linear and quadratic cases of the optimal response functions and uses improving feasible directions to guide the transitions between regions of "simplicity." All can be used with price-directive procedures, but resource-directive optimization has the advantages of primality. 66 pp. Ref.