Theorems on the decomposition of a large nonlinear convex separable economic system in the dual direction |
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Authors: | Carl-Louis Sandblom |
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Institution: | 1. Concordia University, Montreal, Canada
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Abstract: | 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 1] for linear programmes and generalized to nonlinear convex separable programmes by Kronsjö 4] and by Geoffrion 3]. After considering our basic nonlinear programming problem from a two-stage minimization point of view, we review the Kronsjö nonlinear decomposition algorithm. Then we establish some properties of a function related to this algorithm. |
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