A Coordinatewise Domain Scaling Algorithm for M-convex Function Minimization
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
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This paper shows an application of the M-convexs ubmodular flow problem to an economic model in which producers and consumers trade various indivisible commodities through a perfectly divisible commodity, money. We give an efficient algorithm to decide whether a competitive equilibrium exists or not, when cost functions of the producers are M驴-convex and utility functions of the consumers are M驴-concave and quasilinear in money. The algorithm consists of two phases: the first phase computes productions and consumptions in an equilibrium by solving an M-convexs ubmodular flow problem and the second finds an equilibrium price vector by solving a shortest path problem.