求解半无限规划问题的一类新的精确罚函数方法

A New Exact Penalty Function Method for Solving Semi-Infinite Programming Problems

摘要: 对于半无限规划问题，我们提供了一种新的概括性的精确罚函数，它包含了许多常用的罚函数作为特例。我们证明了在适当的约束规格条件下，当罚参数充分大的时候，罚问题的局部最优解也是原问题的局部最优解。另外，在适当的条件下我们证明了罚问题的全局最优解序列收敛于原问题的全局最优解。

Abstract: For semi-infinite programming problems, we provide a new generalized exact penalty function, which contains many commonly used penalty functions as a special case. It is proved that the local optimal solution of the unconstrained optimization subproblem is also the local optimal solution of the original problem when the penalty parameter is sufficiently large under some constraint qualification. Moreover, under suitable conditions, we also prove that the global optimal solution sequence of unconstrained optimization subproblem converges to the global optimal solution of the original problem.