Mathematical programming with iterative aggregation

Mathematical models of economic systems often involve aggregation of variables or requirements. Various authors (especially Dudkin et al.) have applied mathematical programming methods to aggregation models, and have proposed iterative algorithms for computing them. This paper demonstrates the relation between such iterative algorithms and algorithms (developed by Rockafellar) using augmented Lagrangians. A novel iterative aggregation algorithm to solve linear programs is presented. The overall logic and convergence behaviour are derived from the Powell-Hestenes-Rockafellar algorithm.