Abstract
The weighted matroid intersection problem has recently been extended to the valuated matroid intersection problem: Given a pair of valuated matroidsM i = (V, ℬ i , ω i ) (i = 1,2) defined on a common ground setV, find a common baseB ∈ ℬ 1 ∩ ℬ 2 that maximizesω 1 (B) + ω 2 (B). This paper develops a Fenchel-type duality theory related to this problem with a view to establishing a convexity framework for nonlinear integer programming. A Fenchel-type min max theorem and a discrete separation theorem are given. Furthermore, the subdifferentials of matroid valuations are investigated. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
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This work was done while the author was at Forschungsinstitut für Diskrete Mathematik, Universität Bonn, 1994–1995.
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Murota, K. Fenchel-type duality for matroid valuations. Mathematical Programming 82, 357–375 (1998). https://doi.org/10.1007/BF01580075
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DOI: https://doi.org/10.1007/BF01580075