Exact Penalty Methods With Constrained Subproblems

The objective of this paper is twofold. On one hand, the main results of the exact penalty methods for nonlinear programming that are useful for algorithmic purposes are surveyed and the proof of the main result is simplified. On the other hand, it is shown that the main theorem of this subject still holds when one includes only a subset of the constraints in the penalyzed objective function, so that suitable constrained subproblems are solved at each penalty step. The reasons why this is important from a practical (algorithmic) point of view are explained.