Econometrica: Oct 1960, Volume 28, Issue 4

Market Mechanisms and Mathematical Programming

https://doi.org/0012-9682(196010)28:4<872:MMAMP>2.0.CO;2-Q
p. 872-881

Hirofumi Uzawa

In this paper we discuss an application of the competitive mechanisms to mathematical programming. The competitive method was first investigated by Professor Paul A. Samuelson for linear programming and was later applied to concave programming by Professors Kenneth J. Arrow and Leonid Hurwicz. We shall consider two formulations of Walras's tatonnement processes in order to solve programming problems and show that both processes are globally stable for general programming problems in which neither the concavity of the maximands nor the convexity of the feasible sets is necessarily assumed.

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