In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that under Mangasarian–Fromovitz constraint qualification conditions, a local solution of penalty problem is a corresponding local solution of original problem when the penalty parameter is sufficiently large. Furthermore, global convergence properties are shown under some conditions. The paper is concluded with some numerical examples proving the applicability of our methods to PID controller design and linear-phase FIR digital filter design.

中文翻译：

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半无限优化问题的一类精确罚分方法的收敛性质

本文针对半无限优化问题推导了一类新的统一惩罚函数，其中包括许多作为特殊情况的惩罚函数。在Mangasarian–Fromovitz约束限定条件下，当惩罚参数足够大时，惩罚问题的局部解是原始问题的相应局部解，从某种意义上说，它们是正确的。此外，在某些条件下显示了全局收敛性。本文以一些数值算例作为结论，证明了我们的方法在PID控制器设计和线性相位FIR数字滤波器设计中的适用性。