Commodity Exchanges as Gradient Processes
阐明Malinvaud等人的两个动态过程与非线性优化中的梯度投影法之间的关系，基于有效配置的一阶特征建立联系，并提出适用于经典福利最大化问题的新过程。
The purpose here is to make explicit the sense in which two dynamic processes, due to Malinvaud and others (whose solutions determine an efficient allocation for a given economy), are related to the gradient projection method known in the nonlinear optimization literature. The connections we establish derive from simple observations on first order characterizations of efficient allocations; they also lead to the formulation of another process, that applies to a classical welfare maximization problem; finally, they provide a common basis for an a priori justification of each of the three processes involved, which supplements the intrinsic properties that they can be shown to have.