一类新的无参数填充函数及其在最小二乘法中的应用

A New Type of Non-Parameter Filled Function and Its Application in Least Squares

摘要: 针对一般约束优化问题，本文提出了一类新的无参数填充函数，分析该函数的理论性质并设计算法，利用Python编程语言进行数值实验并且与前人结果进行比较，表明该填充函数算法不仅是有效的而且在处理某些函数时效果更好。进一步地，尝试将该算法与化学实验酶促反应的反应速度和反应浓度关系的处理结合，实验结果表明该算法在实际应用中也有较好的适应性。

Abstract: In this paper, a novel non-parameter filled function for solving general constrained global optimi-zation problem is proposed. Then the theoretical properties of the function are argued and corre-sponding algorithm is given in this paper. Numerical experiments using the Python programming language and comparison with previous results show that the proposed filled function algorithm is not only effective but also works better when dealing with certain function. Furthermore, the algorithm is tentatively combined with the treatment of the reaction rate and reactant concentra-tion of the enzymatic reaction of chemical experiments, indicating that the algorithm also has good adaptability in practical cases.