Tropical optimization problems
arXiv:1408.0313
Abstract
We consider optimization problems that are formulated and solved in the framework of tropical mathematics. The problems consist in minimizing or maximizing functionals defined on vectors of finite-dimensional semimodules over idempotent semifields, and may involve constraints in the form of linear equations and inequalities. The objective function can be either a linear function or nonlinear function calculated by means of multiplicative conjugate transposition of vectors. We start with an overview of known tropical optimization problems and solution methods. Then, we formulate certain new problems and present direct solutions to the problems in a closed compact vector form suitable for further analysis and applications. For many problems, the results obtained are complete solutions.
23 Pages. arXiv admin note: text overlap with arXiv:1406.1777
References in corpus (9)
- Tropical linear-fractional programming and parametric mean payoff games
- Extremal properties of tropical eigenvalues and solutions to tropical optimization problems
- The Maslov dequantization, idempotent and tropical mathematics: A brief introduction
- A constrained tropical optimization problem: complete solution and application example
- Algebraic solutions to multidimensional minimax location problems with Chebyshev distance
- Direct solutions to tropical optimization problems with nonlinear objective functions and boundary constraints
- Explicit solution of a tropical optimization problem with application to project scheduling
- A complete closed-form solution to a tropical extremal problem
- A tropical extremal problem with nonlinear objective function and linear inequality constraints