摘要
有些优化问题中的目标函数或者约束函数是分段函数,该类函数不具有连续性和可微性,也即不符合非线性规划问题求解的最优性条件,因而传统的梯度类算法难以求解此类优化问题。利用神经网络较强的非线性映射能力,结合最小二乘法可以进行曲线拟合的特点,提出一种将分段函数处理成具有连续而且可微性的函数的方法。最后进行实例验证,并进行误差分析,结果表明该方法处理得出的连续且可微的函数对分段函数的逼近精度较高,可以利用该函数进行优化求解。
The objective function or constraint function in some optimization problems belongs to piecewise function. Lacking of continuity and differentiability, this function does not conform to the optimality conditions for solving nonlinear programming problems, so the traditional gradient class algorithm can hardly solve such optimization problems. In this paper, by using the strong nonlinear mapping ability of neural network and the characteristics of curve fitting by the least square method, a method of processing piecewise function into a function with continuous and differentiable properties is proposed. Finally, the example verification is carried out and the error analysis is made. The result shows that the continuous and differentiable function obtained by this method has higher approximation accuracy to the piecewise function, and can be used to optimize solution.
作者
冯长敏
张炳江
FENG Changmin;ZHANG Bingjiang(School of Applied Science,Beijing Information Science&Technology University,Beijing 100192,China)
出处
《北京信息科技大学学报（自然科学版）》
2019年第1期18-22,共5页
Journal of Beijing Information Science and Technology University
基金
国家自然科学基金资助项目(11271362)
关键词
BP神经网络
连续化
正态分布
函数逼近
最小二乘法
BP neural network
continuum
normal distribution
function approximation
least square method
