一个新的单参数填充函数及其在非线性数据拟合中的应用
A New Filled Function with One Parameter and Its Application in Nonlinear Data Fitting
DOI: 10.12677/aam.2026.154157, PDF,   
作者: 郑文胜, 张 莹*：浙江师范大学数学科学学院，浙江 金华；曹安维：锐志(宁波)智能科技有限公司，浙江 宁波
关键词: 全局优化；填充函数；非线性数据拟合；Global Optimization； Filled Function； Nonlinear Data Fitting
摘要: 填充函数法是一类求解全局优化问题的高效确定性方法。本文针对无约束全局优化问题，基于填充函数定义，构造了一个新的单参数填充函数，并且给出了相应的填充函数算法，多个经典的数值算例实验结果表明，该算法是有效可行的。同时利用此填充函数处理非线性数据拟合问题，发现相较于传统的非线性回归方法而言，其拟合效果更优。
Abstract: The filled function method is a class of efficient deterministic methods for solving global optimization problems. In this paper, we focus on unconstrained global optimization problems and construct a new filled function with one parameter based on the definition of the filled function. A corresponding filled function algorithm is also presented. Numerical experiments with several classical examples demonstrate the effectiveness and feasibility of the algorithm. Moreover, when this filled function is applied to nonlinear data fitting problems, it is found that the fitting results are superior to those obtained by traditional nonlinear regression methods.
文章引用：郑文胜, 曹安维, 张莹. 一个新的单参数填充函数及其在非线性数据拟合中的应用[J]. 应用数学进展, 2026, 15(4): 286-297. https://doi.org/10.12677/aam.2026.154157

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