择优分配最优化原理及其应用

本文讨论在资源约束条件下如何分配使产出的效果极大。从最简单的两块土地分配化肥使增产的粮食极大化开始,在边际上不断调整,得出一般约束条件下的最优化方法,即拉格朗日乘子法。此优化原理更可以推广到动态过程,借用物理学中的捷降线问题,把落差看成资源,在逐步分配落差中使旅程的时间最短,进而把动态问题一般化,推导出变分法中的欧拉方程。择优分配原理可以将拉氏乘数法和欧拉方程都解释为资源的优化配置问题,从而给出了它们的经济学意义。本方法为一基本的优化原理,有广泛的应用可能。

PRINCIPLE OF OPTIMAL ALLOCATION AND ITS APPLICATIONS

The problem dealt with in this paper is how to allocate resources to achieve maximum effectiveness. Starting from a simple problem, to distribute chemical fertilizer on two plots of land to obtain maximum yield by continuous improvements on the margin, the method of Lagrange Multiplier can be deducted. This idea can be extended to dynamic problems. Borrowing the problem of Brachistochrone, to find a path descending along which a movable particle is to reach a given point in a vertical plane in the shortest ...