TY - JOUR
T1 - Relationship of M-/L-convex functions with discrete convex functions by Miller and Favati-Tardella
AU - Murota, Kazuo
AU - Shioura, Akiyoshi
N1 - Funding Information:
This work is supported by Grant-in-Aid of the Ministry of Education, Science, Sports and Culture of Japan. The authors thank Gyula Károlyi for Example 3.1 , and Satoru Fujishige and Takashi Takabatake for stimulating comments.
PY - 2001/11/15
Y1 - 2001/11/15
N2 - We clarify the relationship of the concepts of M-convex and L-convex functions due to Murota (Adv. Math. 124 (1996); Math. Programming 83 (1998)) with two other concepts of discrete convex functions over integer lattice points, discretely-convex functions due to Miller (SIAM J. Appl. Math. 21 (1971)), and integrally-convex functions due to Favati-Tardella (Ricerca Operativa 53 (1990)). We also investigate whether each class of discrete convex functions is closed under fundamental operations such as addition and convolution.
AB - We clarify the relationship of the concepts of M-convex and L-convex functions due to Murota (Adv. Math. 124 (1996); Math. Programming 83 (1998)) with two other concepts of discrete convex functions over integer lattice points, discretely-convex functions due to Miller (SIAM J. Appl. Math. 21 (1971)), and integrally-convex functions due to Favati-Tardella (Ricerca Operativa 53 (1990)). We also investigate whether each class of discrete convex functions is closed under fundamental operations such as addition and convolution.
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U2 - 10.1016/S0166-218X(01)00222-0
DO - 10.1016/S0166-218X(01)00222-0
M3 - Article
AN - SCOPUS:0035980936
VL - 115
SP - 151
EP - 176
JO - Discrete Applied Mathematics
JF - Discrete Applied Mathematics
SN - 0166-218X
IS - 1-3
ER -