目标函数优化的切线交点法

发布时间：2018-06-25 08:58

本文选题：优化方法 + 切线交点法　；参考：《机械设计与研究》2017年02期

【摘要】：优化方法由数学推演的运用而体现其理论性。牛顿法是理论性最强的一维优化方法,也称为二阶近似式法或导函数切线零点法。类比该方法,以目标函数切线为出发点提出了目标函数切线交点法。采用一定的方法确定导数符号相反的相邻两点,在目标函数曲线上,在对应于该两点处分别做切线,其切线倾斜方向相反,将两条切线平移到表示设计变量的数轴上,令两条切线的交点对应于新点;在三点中确定导数符号相反的相邻两点重复上述运算,直到满足终止条件为止。算例证明,切线交点法的寻优效果比对称等比例区间削去法(黄金分割法)的好,并且可解决牛顿法难以解决的优化问题。
[Abstract]:The optimization method embodies its theory by the application of mathematical deduction. Newton method is the most theoretical one-dimensional optimization method, also known as the second order approximation method or derivative tangent zero point method. By analogy with this method, the tangent point method of objective function is put forward with tangent of objective function as the starting point. Two adjacent points with opposite derivative symbols are determined by a certain method. On the objective function curve, tangent lines are made at the corresponding two points, and the tangent tilting direction is opposite, and the two tangent lines are moved to the number axis representing the design variable. Let the intersection of two tangent lines correspond to the new point, and repeat the above operations at the adjacent two points in which the derivative sign is opposite, until the termination condition is satisfied. The example shows that the tangent intersection method is better than the symmetric equal proportion interval cutting method (golden section method) and can solve the optimization problem which is difficult to be solved by Newton method.
【作者单位】：中国石油大学(华东)中国石油大学胜利学院;东营市胜利第二中学;东营市胜利第三中学;
【基金】：山东省自然科学基金资助项目(Q2006A08)
【分类号】：O224

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