Algebraic solutions of tropical optimization problems
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2014
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| _version_ | 1866909075050070016 |
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| author | Krivulin, N. |
| author_facet | Krivulin, N. |
| contents | We consider multidimensional optimization problems, which are formulated and solved in terms of tropical mathematics. The problems are to minimize (maximize) a linear or nonlinear function defined on vectors over an idempotent semifield, and may have constraints in the form of linear equations and inequalities. The aim of the paper is twofold: first to give a broad overview of known tropical optimization problems and solution methods, including recent results; and second, to derive a direct, complete solution to a new constrained optimization problem as an illustration of the algebraic approach recently proposed to solve tropical optimization problems with nonlinear objective functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1406_1777 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | Algebraic solutions of tropical optimization problems Krivulin, N. Optimization and Control Systems and Control 65K05 (Primary), 15A80, 90C48, 65K10 (Secondary) We consider multidimensional optimization problems, which are formulated and solved in terms of tropical mathematics. The problems are to minimize (maximize) a linear or nonlinear function defined on vectors over an idempotent semifield, and may have constraints in the form of linear equations and inequalities. The aim of the paper is twofold: first to give a broad overview of known tropical optimization problems and solution methods, including recent results; and second, to derive a direct, complete solution to a new constrained optimization problem as an illustration of the algebraic approach recently proposed to solve tropical optimization problems with nonlinear objective functions. |
| title | Algebraic solutions of tropical optimization problems |
| topic | Optimization and Control Systems and Control 65K05 (Primary), 15A80, 90C48, 65K10 (Secondary) |
| url | https://arxiv.org/abs/1406.1777 |