arXiv:1408.0313math.OC
Tropical optimization problems
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
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.
I haven’t read it but I would guess this is a good place to start: https://arxiv.org/abs/1408.0313 My familiarity with tropical geometry is mostly conversational :) and entirely on the pure math side. The basic definitions use obviously lend themselves to optimization problems…
nicklecompteView on HNParent context