TY - JOUR
T1 - Proximity theorems of discrete convex functions
AU - Murota, Kazuo
AU - Tamura, Akihisa
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2004/4
Y1 - 2004/4
N2 - A proximity theorem is a statement that, given an optimization problem and its relaxation, an optimal solution to the original problem exists in a certain neighborhood of a solution to the relaxation. Proximity theorems have been used successfully, for example, in designing efficient algorithms for discrete resource allocation problems. After reviewing the recent results for L-convex and M-convex functions, this paper establishes proximity theorems for larger classes of discrete convex functions, L2-convex functions and M 2-convex functions, that are relevant to the polymatroid intersection problem and the submodular flow problem.
AB - A proximity theorem is a statement that, given an optimization problem and its relaxation, an optimal solution to the original problem exists in a certain neighborhood of a solution to the relaxation. Proximity theorems have been used successfully, for example, in designing efficient algorithms for discrete resource allocation problems. After reviewing the recent results for L-convex and M-convex functions, this paper establishes proximity theorems for larger classes of discrete convex functions, L2-convex functions and M 2-convex functions, that are relevant to the polymatroid intersection problem and the submodular flow problem.
KW - Discrete convex analysis
KW - Optimality criteria
KW - Proximity properties
UR - http://www.scopus.com/inward/record.url?scp=21144451016&partnerID=8YFLogxK
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U2 - 10.1007/s10107-003-0466-7
DO - 10.1007/s10107-003-0466-7
M3 - Article
AN - SCOPUS:21144451016
VL - 99
SP - 539
EP - 562
JO - Mathematical Programming
JF - Mathematical Programming
SN - 0025-5610
IS - 3
ER -