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A formulation of combinatorial auction via reverse convex programming. (English) Zbl 1116.90090
Summary: In combinatorial auctions, buyers and sellers bid not only for single items but also for combinations (or bundles, or baskets) of items. Clearing the auction is in general an NP-hard problem; it is usually solved with integer linear programming. We proposed in an earlier paper a continuous approximation of this problem, where orders are aggregated and integrality constraints are relaxed. It was proved that this problem could be solved efficiently in two steps by calculating two fixed points, first the fixed point of a contraction mapping, and then of a set-valued function. In this paper, we generalize the problem to incorporate constraints on maximum price changes between two auction rounds. This generalized problem cannot be solved by the aforementioned methods and necessitates reverse convex programming techniques.
MSC:
90C27 Combinatorial optimization
90C10 Integer programming
90C25 Convex programming
91A46 Combinatorial games
91B26 Auctions, bargaining, bidding and selling, and other market models
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