### Abstract

In broadcast channels, network utility maximization formulates a scheduling problem in order to maximize a sum of given utility functions. It is known that the network utility maximization is achieved if a gradient method is used. In this paper, however, we show that the network utility maximization is achieved only if a gradient method is used. That proves the equivalence between a problem formulated by the network utility maximization and a problem with a gradient method. The gradient method simplifies the object function of a scheduling problem by modifying utility functions to a gradient form, so that it makes easy to deal with the problem. We apply the gradient method to a problem with utility functions given by generalized proportional fairness. It is revealed that using the gradient method for the generalized proportional fairness is equivalent to applying a binomial approximation. Simulation results are presented with various scheduling parameters.

Original language | English |
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Title of host publication | 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Proceedings |

DOIs | |

Publication status | Published - 2011 Aug 29 |

Event | 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Budapest, Hungary Duration: 2011 May 15 → 2011 May 18 |

### Other

Other | 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring |
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Country | Hungary |

City | Budapest |

Period | 11/5/15 → 11/5/18 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Proceedings*[5956391] https://doi.org/10.1109/VETECS.2011.5956391

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*2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Proceedings.*, 5956391, 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring, Budapest, Hungary, 11/5/15. https://doi.org/10.1109/VETECS.2011.5956391

**Direct derivation of the gradient method for network utility maximization in broadcast channels and its application.** / Joung, Heejin; Mun, Cheol; Ko, Jae Yun; Yook, Jong Gwan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Direct derivation of the gradient method for network utility maximization in broadcast channels and its application

AU - Joung, Heejin

AU - Mun, Cheol

AU - Ko, Jae Yun

AU - Yook, Jong Gwan

PY - 2011/8/29

Y1 - 2011/8/29

N2 - In broadcast channels, network utility maximization formulates a scheduling problem in order to maximize a sum of given utility functions. It is known that the network utility maximization is achieved if a gradient method is used. In this paper, however, we show that the network utility maximization is achieved only if a gradient method is used. That proves the equivalence between a problem formulated by the network utility maximization and a problem with a gradient method. The gradient method simplifies the object function of a scheduling problem by modifying utility functions to a gradient form, so that it makes easy to deal with the problem. We apply the gradient method to a problem with utility functions given by generalized proportional fairness. It is revealed that using the gradient method for the generalized proportional fairness is equivalent to applying a binomial approximation. Simulation results are presented with various scheduling parameters.

AB - In broadcast channels, network utility maximization formulates a scheduling problem in order to maximize a sum of given utility functions. It is known that the network utility maximization is achieved if a gradient method is used. In this paper, however, we show that the network utility maximization is achieved only if a gradient method is used. That proves the equivalence between a problem formulated by the network utility maximization and a problem with a gradient method. The gradient method simplifies the object function of a scheduling problem by modifying utility functions to a gradient form, so that it makes easy to deal with the problem. We apply the gradient method to a problem with utility functions given by generalized proportional fairness. It is revealed that using the gradient method for the generalized proportional fairness is equivalent to applying a binomial approximation. Simulation results are presented with various scheduling parameters.

UR - http://www.scopus.com/inward/record.url?scp=80051968182&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051968182&partnerID=8YFLogxK

U2 - 10.1109/VETECS.2011.5956391

DO - 10.1109/VETECS.2011.5956391

M3 - Conference contribution

AN - SCOPUS:80051968182

SN - 9781424483310

BT - 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Proceedings

ER -