Geodesic
Complete solution of tropical vector inequalities using matrix sparsification
Applications of Mathematics, Tome 65 (2020) no. 6, pp. 755-775 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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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     title = {Complete solution of tropical vector inequalities using matrix sparsification},
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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

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