Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables
Summary :
The concepts of M-convexity and L-convexity, introduced by Murota (1996, 1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota-Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental properties of general M-convex and L-convex functions.
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- IEICE TRANSACTIONS on Fundamentals Vol.E87-A No.5 pp.1042-1052
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- 2004/05/01
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- Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
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Kazuo MUROTA, Akiyoshi SHIOURA, "Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables" in IEICE TRANSACTIONS on Fundamentals,
vol. E87-A, no. 5, pp. 1042-1052, May 2004, doi: .
Abstract: The concepts of M-convexity and L-convexity, introduced by Murota (1996, 1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota-Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental properties of general M-convex and L-convex functions.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e87-a_5_1042/_p
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@ARTICLE{e87-a_5_1042,
author={Kazuo MUROTA, Akiyoshi SHIOURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables},
year={2004},
volume={E87-A},
number={5},
pages={1042-1052},
abstract={The concepts of M-convexity and L-convexity, introduced by Murota (1996, 1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota-Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental properties of general M-convex and L-convex functions.},
keywords={},
doi={},
ISSN={},
month={May},}
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TY - JOUR
TI - Fundamental Properties of M-Convex and L-Convex Functions in Continuous Variables
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1042
EP - 1052
AU - Kazuo MUROTA
AU - Akiyoshi SHIOURA
PY - 2004
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E87-A
IS - 5
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - May 2004
AB - The concepts of M-convexity and L-convexity, introduced by Murota (1996, 1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota-Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental properties of general M-convex and L-convex functions.
ER -
English
