Theorems on the decomposition of a large nonlinear convex separable economic system in the dual direction

✍ Scribed by Carl-Louis Sandblom

• Publisher: Springer US
• Year: 1978
• Tongue: English
• Weight: 319 KB
• Volume: 14
• Category: Article
• ISSN: 1573-9414
• DOI: 10.1007/bf00150380

✦ Synopsis

Large mathematical programming problems often arise as the result of the economic planning process. When such a problem is not only large, but nonlinear as well, there is a need to make it more manageable by breaking it down into several smaller and more easily handled subproblems. The subproblems are solved separately with the coordination activity carried out by a "master problem". A decomposition method can be seen as a "dialogue" between the master problem and the subproblems, where the flow of information back and forth between the former and the latters results in a series of approximations converging to the solution of the overall problem. Such a decomposition method was elaborated by Benders [I] for linear programmes and generalized to nonlinear convex separable programmes by Kronsj6 [4] and by Geoffrion [3]. After considering our basic nonlinear programming problem from a two-stage minimization point of view, we review the Kronsj6 nonlinear decomposition algorithm. Then we establish some properties of a function related to this algorithm. * I am grateful to Professor T.O.M. Kronsj6 for inspiring this work and giving valuable help.