Geodesic
Complete solution of tropical vector inequalities using matrix sparsification
Applications of Mathematics, Tome 65 (2020) no. 6, pp. 755-775.

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We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that uses sparse matrices to simplify the problem and to construct a family of solution sets, each defined by a sparse matrix obtained from one of the given matrices by setting some of its entries to zero. All solutions are then combined to present the result in a parametric form in terms of a matrix whose columns form a complete system of generators for the solution. We describe the computational technique proposed to solve the problem, remark on its computational complexity and illustrate this technique with numerical examples.
DOI : 10.21136/AM.2020.0376-19
Classification : 15A39, 15A80, 65F50
Keywords: tropical semifield; tropical two-sided inequality; matrix sparsification; complete solution; backtracking 
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Krivulin, Nikolai. Complete solution of tropical vector inequalities using matrix sparsification. Applications of Mathematics, Tome 65 (2020) no. 6, pp. 755-775. doi : 10.21136/AM.2020.0376-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0376-19/

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