Examples of max-flow and min-cut problems with duality gaps in continuous networks

Examples of max-flow and min-cut problems with duality gaps in continuous networks

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Article ID: iaor19951845
Country: Netherlands
Volume: 63
Issue: 2
Start Page Number: 213
End Page Number: 234
Publication Date: Jan 1994
Journal: Mathematical Programming (Series A)
Authors:
Keywords: duality
Abstract:

Strang gave a method to establish a max-flow min-cut theorem in a domain of a Euclidean space. The method can be applied also to max-flow min-cut problems defined by Iri whenever the capacity functions of max-flow problems are bounded and continuous. This paper deals with max-flow min-cut problems of Strang and Iri with unbounded or noncontinuous capacity functions. It is proved that, in such problems, max-flow min-cut theorems may fail to hold.

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