一类资源最优配置的充要条件及其应用

Necessary and Sufficient Condition of a Kind of Resource Optimal Allocation with Application

本文研究了由工业投资、教育投资等问题中导出的一类非线性规划问题,应用Kuhn-Tucher定理得到了Rn中向量x=(x1,x2,…,xn)是这问题最优解的充分必要条件．应用这一结果导出了求解一类资源最优配置问题的新算法．这是一个具有计算复杂度为O(mn(m+n))的多项式型算法．

In this paper we study a kind of nonlinear programming problems derived from various investment problems like industral production investment, educational investment...etc. Appling Kuhn-Tucher theorem obtain a necessary end sufficient condition for a vector x = （x1,…,xn） ∈ R^n to be a optimal solution of the nonlinear programming problems.From this result, a new alogrithm to sovle a kind of resource optimal allocation problems is derived, The alogrithm is polynomal alogrithm with complexity O（mn（m ＋ n））.