### Abstract

Original language | English |
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Pages | 38-38 |

Publication status | Published - Aug 2018 |

Event | Modeling and Optimization: Theory and Applications - Lehigh University, Bethlehem Duration: 15 Aug 2018 → 17 Aug 2018 http://coral.ie.lehigh.edu/~mopta/ |

### Conference

Conference | Modeling and Optimization: Theory and Applications |
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Abbreviated title | MOPTA 2018 |

Country | United States |

City | Bethlehem |

Period | 15/08/18 → 17/08/18 |

Internet address |

### Fingerprint

### Scopus subject areas

- Control and Optimization
- Algebra and Number Theory
- Management Science and Operations Research

### Cite this

*Tropical optimization problems: recent results and applications examples*. 38-38. Abstract from Modeling and Optimization: Theory and Applications, Bethlehem, .

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**Tropical optimization problems: recent results and applications examples.** / Кривулин, Николай Кимович.

Research output

TY - CONF

T1 - Tropical optimization problems: recent results and applications examples

AU - Кривулин, Николай Кимович

PY - 2018/8

Y1 - 2018/8

N2 - We consider multidimensional optimization problems formulated in the tropical mathematics setting to minimize or maximize functions defined on vectors over idempotent semifields, subject to linear equality and inequality constraints. We start with a brief overview of known tropical optimization problems and solution approaches. Furthermore, some new problems are presented with nonlinear objective functions calculated using multiplicative conjugate transposition of vectors, including problems of Chebyshev approximation, problems of approximation in the Hilbert seminorm, and pseudo-quadratic problems. To solve these problems, we apply methods based on the reduction to the solution of parametrized inequalities, matrix sparsification, and other techniques. The methods offer direct solutions represented in a compact explicit vector form ready for further analysis and straightforward computation. We conclude with a short discussion of the application of the results obtained to practical problems in location analysis, project scheduling and decision making.

AB - We consider multidimensional optimization problems formulated in the tropical mathematics setting to minimize or maximize functions defined on vectors over idempotent semifields, subject to linear equality and inequality constraints. We start with a brief overview of known tropical optimization problems and solution approaches. Furthermore, some new problems are presented with nonlinear objective functions calculated using multiplicative conjugate transposition of vectors, including problems of Chebyshev approximation, problems of approximation in the Hilbert seminorm, and pseudo-quadratic problems. To solve these problems, we apply methods based on the reduction to the solution of parametrized inequalities, matrix sparsification, and other techniques. The methods offer direct solutions represented in a compact explicit vector form ready for further analysis and straightforward computation. We conclude with a short discussion of the application of the results obtained to practical problems in location analysis, project scheduling and decision making.

M3 - Abstract

SP - 38

EP - 38

ER -