We present a general theory of exact penalty functions with vectorial (multidimensional) penalty parameter for optimization problems in infinite dimensional spaces. In comparison with the scalar case, the use of vectorial penalty parameters provides much more flexibility, allows one to adaptively and independently take into account the violation of each constraint during optimization process, and often leads to a better overall performance of an optimization method using an exact penalty function. We obtain sufficient conditions for the local and global exactness of penalty functions with vectorial penalty parameters and study convergence of global exact penalty methods with several different penalty updating strategies. In particular, we present a new algorithmic approach to an analysis of the global exactness of penalty functions, which contains a novel characterisation of the global exactness property in terms of behaviour of sequences generated by certain optimization methods.

我们针对无限维空间中的优化问题提出了具有矢量（多维）惩罚参数的精确惩罚函数的一般理论。与标量情况相比，向量惩罚参数的使用提供了更大的灵活性，允许在优化过程中自适应地和独立地考虑每个约束的违反，并且通常会导致使用一个优化方法的更好的整体性能精确的惩罚函数。我们获得了具有向量惩罚参数的惩罚函数的局部和全局精确性的充分条件，并研究了具有几种不同惩罚更新策略的全局精确惩罚方法的收敛性。特别是，我们提出了一种新的算法方法来分析惩罚函数的全局准确性，