Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 539-562 |
| Number of pages | 24 |
| Journal | Mathematical Programming |
| Volume | 99 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2004 Apr |
| Externally published | Yes |
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Keywords
- Discrete convex analysis
- Optimality criteria
- Proximity properties
ASJC Scopus subject areas
- Applied Mathematics
- Mathematics(all)
- Safety, Risk, Reliability and Quality
- Management Science and Operations Research
- Software
- Computer Graphics and Computer-Aided Design
- Computer Science(all)
Cite this
Proximity theorems of discrete convex functions. / Murota, Kazuo; Tamura, Akihisa.
In: Mathematical Programming, Vol. 99, No. 3, 04.2004, p. 539-562.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Proximity theorems of discrete convex functions
AU - Murota, Kazuo
AU - Tamura, Akihisa
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
UR - http://www.scopus.com/inward/citedby.url?scp=21144451016&partnerID=8YFLogxK
U2 - 10.1007/s10107-003-0466-7
DO - 10.1007/s10107-003-0466-7
M3 - Article
VL - 99
SP - 539
EP - 562
JO - Mathematical Programming
JF - Mathematical Programming
SN - 0025-5610
IS - 3
ER -