Article ID: | iaor1988185 |
Country: | United States |
Volume: | 13 |
Issue: | 3 |
Start Page Number: | 435 |
End Page Number: | 446 |
Publication Date: | Aug 1988 |
Journal: | Mathematics of Operations Research |
Authors: | Qi Liqun |
Three set-function classes more general than submodular ones are discussed. An odd submodular function defines a box totally dual integral system. An integral odd submodular function and its Dilworth truncation, i.e., a Dilworth function, give rise to the same polyhedron with integral vertices. The minimum of two submodular functions is an odd submodular function. The convolution of two submodular functions is a Dilworth function. A Dilworth function is a discrete convex function. A discrete convex function can be characterized by its convex hull, subgradients, epigraph and general subadditivity. Discrete convexity is preserved under many natural operations.