In this article, a class of lower-order smoothed objective penalty functions is introduced to find locally optimal points for constrained optimization problems. The exactness of the new penalty functions is studied. Based on the current locally optimal points, a new class of penalty functions based on filling properties is proposed. This new penalty function can be used to find a better locally optimal point. The exactness and filling properties of this penalty function are proved in this paper. To do this, two algorithms are presented to find the locally and globally optimal points. Additionally, their convergence is proved under some mild conditions. Finally, numerical results are included to illustrate the applicability of the local and global optimization algorithms.

在本文中，引入了一类低阶平滑目标惩罚函数来寻找约束优化问题的局部最优点。研究了新惩罚函数的准确性。基于当前局部最优点，提出了一类新的基于填充特性的惩罚函数。这个新的惩罚函数可以用来找到更好的局部最优点。本文证明了该惩罚函数的正确性和填充性。为此，提出了两种算法来找到局部和全局最优点。此外，它们的收敛性在一些温和的条件下得到证明。最后，包括数值结果来说明局部和全局优化算法的适用性。