Algebraic solutions of tropical optimization problems
arXiv:1406.1777 · doi:10.1134/S199508021504006X
Abstract
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.
16 pages, presented at Intern. Conf. "Algebra and Mathematical Logic: Theory and Applications", June 2-6, 2014, Kazan, Russia
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