Algebraic solutions of tropical optimization problems
For researchers in tropical mathematics, this paper offers a comprehensive survey and a new solution method for constrained optimization problems.
This paper provides a broad overview of tropical optimization problems and solution methods, and derives a direct, complete solution to a new constrained optimization problem using an algebraic approach.
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.