可微无约束全局优化问题的一种新的无参数填充函数法

A New Non-Parameter Filled Function Method for Differentiable Unconstrained Global Optimization Problems

摘要: 填充函数法在求解全局优化问题中有广泛的应用，此方法利用目标函数的局部性质搜索局部极小点，并通过构造填充函数避免陷入局部极小，通过极小化过程和填充过程的迭代，直到满足终止条件，得到问题的全局极小点。本文提出了一个新的求解无约束全局优化问题的无参数填充函数，其局部极小点与目标函数相同，能够减少算法计算量。在合理的假设条件下，证明该函数的填充性质和相关性质，并设计相应的算法，利用经典算例进行实验，表明该算法是有效可行的。

Abstract: The filled function method has a wide range of applications in solving global optimization problems. This method utilizes the local properties of the objective function to search for local minima, and avoids getting stuck in local minima by constructing a filled function. Through the iteration of the minimization process and filled process until the termination condition is satisfied, the global minima of the problem is obtained. In this paper, we propose a new parameter free filled function, whose local minima are the same as the objective function, which can reduce the computational complexity of the algorithm. Based on reasonable assumptions, we discuss the theoretical properties of the filled function, and develop a corresponding algorithm. Numerical experiments demonstrate the algorithm’s effectiveness and feasibility.