A Cutting Plane Method for Analytical Target Cascading With Augmented Lagrangian Coordination

Various decomposition and coordination methodologies for solving large-scale system design problems have been developed and studied during the past few decades. However, there is generally no guarantee that they will converge to the expected optimum design under general assumptions. Those with proven convergence often have restricted hypotheses or a prohibitive cost related to the required computational effort. Therefore there is still a need for improved, mathematically grounded, decomposition and coordination techniques that will achieve convergence while remaining robust, flexible and easy to implement. In recent years, classical Lagrangian and augmented Lagrangian methods have received renewed interest when applied to decomposed design problems. Some methods are implemented using a subgradient optimization algorithm whose performance is highly dependent on the type of dual update of the iterative process. This paper reports on the implementation of a cutting plane approach in conjunction with Lagrangian coordination and the comparison of its performance with other subgradient update methods. The method is demonstrated on design problems that are decomposable according to the analytic target cascading (ATC) scheme.