The separation theorem in discrete convex analysis states that two disjoint discrete convex sets can be separated by a hyperplane with a 0-1 normal vector. We apply this theorem to an auction model and provide a unified approach to existing results. When p is not an equilibrium price vector,...

Using a notion of convexity in discrete convex analysis, we introduce a discrete analogue of the Kuhn-Tucker theorem. We apply it to an auction model and show that existing iterative auctions can be viewed as the process of finding a saddle point of the Lagrange function.

Using a notion of convexity in discrete convex analysis, we introduce a discrete analogue of the Kuhn-Tucker theorem. We apply it to an auction model and show that existing iterative auctions can be viewed as the process of finding a saddle point of the Lagrange function.