### Abstract

Original language | English |
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Pages | 91 |

Publication status | Published - Jul 2016 |

Event | 20th Conference of the International Linear Algebra Society - KU Leuven, Leuven Duration: 11 Jul 2016 → 15 Jul 2016 https://ilas2016.cs.kuleuven.be/ |

### Conference

Conference | 20th Conference of the International Linear Algebra Society |
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Abbreviated title | ILAS2016 |

Country | Belgium |

City | Leuven |

Period | 11/07/16 → 15/07/16 |

Internet address |

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### Cite this

*Tropical optimization techniques for solving minimax location problems with Chebyshev and rectilinear distances*. 91. Abstract from 20th Conference of the International Linear Algebra Society, Leuven, .

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**Tropical optimization techniques for solving minimax location problems with Chebyshev and rectilinear distances.** / Кривулин, Николай Кимович.

Research output

TY - CONF

T1 - Tropical optimization techniques for solving minimax location problems with Chebyshev and rectilinear distances

AU - Кривулин, Николай Кимович

N1 - Book of Abstracts. 20th ILAS Conference, 11—15 July 2016, KU Leuven

PY - 2016/7

Y1 - 2016/7

N2 - We propose new algebraic solutions for constrained minimax single-facility location problems in multidimensional spaces with Chebyshev distance, and in the plane with rectilinear distance. We first formulate the location problems in a standard form, and outline existing solutions. Then, the problems are represented in terms of tropical (idempotent) algebra as optimization problems to minimize non-linear objective functions defined on vectors over an idempotent semifield, subject to linear vector inequality and equality constraints. We apply methods and techniques of tropical optimization to obtain direct, explicit solutions of the problems. The results obtained are used to derive solutions of the location problems under consideration in a closed form, which is ready for formal analysis and straightforward computation. We examine extensions of the approach to handle other problems, such as rectilinear single-facility location in high-dimensional spaces and multi-facility location. To illustrate, we present numerical solutions of example location problems and provide graphical representation of these solutions.

AB - We propose new algebraic solutions for constrained minimax single-facility location problems in multidimensional spaces with Chebyshev distance, and in the plane with rectilinear distance. We first formulate the location problems in a standard form, and outline existing solutions. Then, the problems are represented in terms of tropical (idempotent) algebra as optimization problems to minimize non-linear objective functions defined on vectors over an idempotent semifield, subject to linear vector inequality and equality constraints. We apply methods and techniques of tropical optimization to obtain direct, explicit solutions of the problems. The results obtained are used to derive solutions of the location problems under consideration in a closed form, which is ready for formal analysis and straightforward computation. We examine extensions of the approach to handle other problems, such as rectilinear single-facility location in high-dimensional spaces and multi-facility location. To illustrate, we present numerical solutions of example location problems and provide graphical representation of these solutions.

M3 - Abstract

SP - 91

ER -