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• W1617680143 abstract "Given a n × n matrix B = (bij) with real entries, the optimal assignment problem is to find a permutationof {1,...,n} maximising the sum P n=1 bi�(i). In discrete optimal control and in the theory of discrete event systems, one often encounters the problem of solving the equation Bf = g for a given vector g, where the same symbol B denotes the corresponding max- plus linear operator, (Bf)i := max1≤j≤n bij + fj. The matrix B is said to be strongly regular when there exists a vector g such that the equation Bf = g has a unique solution f. A result of Butkoviyc and Hevery shows that B is strongly regular if and only if the associated optimal assignment problem has a unique solution. We establish here an extension of this result which applies to max-plus linear operators over a countable state space. The proofs use the theory developed in a previous work in which we characterised the unique solvability of equations involving Moreau conjugacies over an infinite state space, in terms of the minimality of certain coverings of the state space by generalised subdifferentials." @default.
• W1617680143 created "2016-06-24" @default.
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• W1617680143 date "2009-01-01" @default.
• W1617680143 modified "2023-09-28" @default.
• W1617680143 title "The optimal assignment problem for a countable state space" @default.
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• W1617680143 doi "https://doi.org/10.1090/conm/495/09690" @default.
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