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On max-plus two-sided linear systems whose solution sets are min-plus linear - MaRDI portal

On max-plus two-sided linear systems whose solution sets are min-plus linear (Q6541333)

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scientific article; zbMATH DE number 7850922
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On max-plus two-sided linear systems whose solution sets are min-plus linear
scientific article; zbMATH DE number 7850922

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    On max-plus two-sided linear systems whose solution sets are min-plus linear (English)
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    17 May 2024
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    The paper focuses on max-plus two-sided linear systems and the solutions derived from the alternating method. Stable solutions are crucial for understanding the algorithm's behavior.\N\NThe authors highlight the necessity of restricting the solution set to finite entries to maintain boundedness within the max-plus projective space. They prove that the vectors generated by the alternating method span the smallest min-plus linear subspace that encompasses all solutions.\N\NA criterion for the min-plus linearity of the solution set, highlighting its connection to local min-plus convexity, is also introduced. It allows the authors to identify specific conditions that can lead to a failure of local min-plus convexity. Finally, the authors verify that convexity for the vectors generated by the alternating method ensures the min-plus linearity of the solution set. They also provide essential references and foundational concepts for a clear understanding of the topic.
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    linear system
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    convex set
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    tropical semiring
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    alternating method
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