TY - JOUR
T1 - On convolution of L-convex functions
AU - Tamura, Akihisa
N1 - Funding Information:
The author expresses gratitude to Kazuo Murota for his valuable comments. This work is supported by a Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
PY - 2003/4
Y1 - 2003/4
N2 - L2-convex functions, which are the convolution of two L-convex functions, constitute a wide class of discrete convex functions in discrete convex analysis, a unified framework of discrete optimization, proposed by Murota. This article shows a technical result that any L2-convex function can be represented by the convolution of two L-convex functions attaining the infimum in the definition of the convolution. This result gives simple proofs for several known results on L2-convex functions.
AB - L2-convex functions, which are the convolution of two L-convex functions, constitute a wide class of discrete convex functions in discrete convex analysis, a unified framework of discrete optimization, proposed by Murota. This article shows a technical result that any L2-convex function can be represented by the convolution of two L-convex functions attaining the infimum in the definition of the convolution. This result gives simple proofs for several known results on L2-convex functions.
KW - Convolution
KW - Discrete convex analysis
KW - L-/L-convex functions
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U2 - 10.1080/1055678031000074508
DO - 10.1080/1055678031000074508
M3 - Article
AN - SCOPUS:0038487292
SN - 1055-6788
VL - 18
SP - 231
EP - 245
JO - Optimization Methods and Software
JF - Optimization Methods and Software
IS - 2
ER -