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• W4313367967 abstract "We introduce a new class of inverse optimization problems in which an input solution is given together with k linear weight functions, and the goal is to modify the weights by the same deviation vector p so that the input solution becomes optimal with respect to each of them, while minimizing ‖p‖1. In particular, we concentrate on three problems with multiple weight functions: the inverse shortest s−t path, the inverse bipartite perfect matching, and the inverse arborescence problems. Using LP duality, we give min–max characterizations for the ℓ1-norm of an optimal deviation vector. Furthermore, we show that the optimal p is not necessarily integral even when the weight functions are so, therefore computing an optimal solution is significantly more difficult than for the single-weighted case. We also give a necessary and sufficient condition for the existence of an optimal deviation vector that changes the values only on the elements of the input solution, thus giving a unified understanding of previous results on arborescences and matchings." @default.
• W4313367967 created "2023-01-06" @default.
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• W4313367967 date "2023-03-01" @default.
• W4313367967 modified "2023-10-18" @default.
• W4313367967 title "Inverse optimization problems with multiple weight functions" @default.
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• W4313367967 doi "https://doi.org/10.1016/j.dam.2022.12.004" @default.
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