最优化算法的收敛准则

收敛准则是最优化算法的重要组成部分，其选择得好与坏将直接影响到算法的成功与否以及收敛得快与慢。现有常用的收敛准则基本上是建立在前后迭代点的逼近和它们相应函数值的逼近是否达到一定的精度要求以及迭代点处函数梯度是否接近于零的基础上的。它们各自有自己的适用范围。但它们的共同特点是对迭代终止点的性质不能做出判断。本文在总结和分析现有算法收敛准则的基础上，借助于正定矩阵、一维优化方法中对分法和黄金分割法，提出了新的算法收敛准则。算例结果表明，这些收敛准则是有效实用的。

Convergence criteria of optimization algorithm

Convergence criterion is an important component in algorithms for optimization, the good or bad choice of the convergence criteria will directly affect the success or failure of algorithms for optimization as well as the rapid or slow convergence characteristic of them. The existing general used convergence criteria are almost established on the basis of the approaching degree between the front and the back iteration points and their relative functional values as well as the approaching degree of the gradient of the iteration point to zero. They have their own scopes of application. But their common characteristic is fail to make judgement for the nature of iteration stopping point. However the extreme purpose of algorithms for optimization is to get extreme point instead of standing point. Therefore this paper puts forward new convergence criteria with the aid of the positive definite matrix, half-division method and the 0.618 method which are used in one-dimension optimization on the basis of the summarization and analysis of the existing general used convergence criteria for optimization. Finally the results of given examples show that these new convergence criteria is effective and applicabe.