@article{oai:ynu.repo.nii.ac.jp:00002032,
 author = {Ui, Takashi},
 issue = {1},
 journal = {Japan Journal of Industrial and Applied Mathematics},
 month = {Feb},
 note = {application/pdf, postprint, One of the most important properties of a convex function is that a local optimum is also a global optimum. This paper explores the discrete analogue of this property. We consider arbitrary locality in a discrete space and the corresponding local optimum of a function over the discrete space. We introduce the corresponding notion of discrete convexity and show that the local optimum of a function satisfying the discrete convexity is also a global optimum. The special cases include discretely-convex, integrally-convex, M-convex, W-convex, L-convex, and -convex functions.},
 pages = {21--29},
 title = {A note on discrete convexity and local optimality},
 volume = {23},
 year = {2006}
}