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We examine the problem of finding all solutions of two-sided vectorinequalities given in the tropical algebra setting, where the unknown vectormultiplied by known matrices appears on both sides of the inequality. We offera solution that uses sparse matrices to simplify the problem and to construct afamily of solution sets, each defined by a sparse matrix obtained from one ofthe given matrices by setting some of its entries to zero. All solutions arethen combined to present the result in a parametric form in terms of a matrixwhose columns form a complete system of generators for the solution. Wedescribe the computational technique proposed to solve the problem, remark onits computational complexity and illustrate this technique with numericalexamples.

Complete solution of tropical vector inequalities using matrix sparsification