相对微分/差分法搜索非线性规划极值点的充分条件

求解非线性规划有两个问题：一是采用搜索算法时如何判断搜索的结束，二是如何确定所得到的解是局部最优解还是全局最优解．过去一般基于容许误差法解决第一个问题，而第二个问题迄今没有解决．为此给出了两个极值点的充分条件，这是解决第一个问题的一个新方法；给出了判断局部极值点和全局极值点的方法，解决了第二个问题．应用相对微分／差分法解连续和离散非线性规划，在搜索过程中一旦满足了两个充分条件之一，就达到了极值点．根据搜索方向很容易确定极值点是极大点还是极小点．算例表明这两个充分条件对结束搜索有着实用意义．

Sufficient conditions for stationary points of nonlinear programmings with relative differential/difference searching approach

So far there have been two kinds of problems for solving the nonlinear programmings: one is to decide under what criterion to terminate the searching procedure when a certain algorithm is adopted;the other is to determine whether the obtained solution is a local optimum or a global optimum.In the past,the method of allowable error was adopted for the first kind of problem,whereas there have not been feasible methods for the second kind.Two sufficient conditions are presented for stationary solutions.These conditions can be adopted as a new approach to the first kind of problem and used to solve the second kind of problem of identifying the local and global optima.When the relative differential/difference searching approach is implemented for solution of nonlinear continuous and discrete programmings,a stationary point is determined once the conditions are satisfied in the searching procedure.Based on the searching direction,it is easy to identify if the point is the maximum point or the minimum point of the programming.These sufficient conditions are practically important to the termination of the searching procedure.