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Note on Multimodularity and L-Convexity

Graduate School of Information Science and Technology, University of Tokyo, Tokyo 113-8656, Japan
murota{at}mist.i.u-tokyo.ac.jp

Multimodular functions and L-convex functions have been investigated almost independently, but they are, in fact, equivalent objects that can be related through a unimodular coordinate transformation. Some facts known for L-convex functions can be translated to new results for multimodular functions, and vice versa. In particular, the local optimality condition for global optimality found in the literature of multimodular functions should be rectified, and a discrete separation theorem holds for multimodular functions.

Key Words: discrete convex function; multimodular function; L-convex function; local optimality
History: Received: June 6, 2004; revision received: October 17, 2004;

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