A formulation of combinatorial auction via reverse convex programming

A formulation of combinatorial auction via reverse convex programming

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Article ID: iaor2006655
Country: India
Issue: 1
Start Page Number: 19
End Page Number: 32
Publication Date: Apr 2005
Journal: Journal of Applied Mathematics & Decision Sciences
Authors:
Keywords: programming: convex, programming: integer
Abstract:

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.

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