New active set identification for general constrained optimization and minimax problems

The purpose of this paper is to discuss the problem of identifying the active constraints for general constrained nonlinear programming and constrained minimax problems at an isolated local solution. Facchinei, Fischer and Kanzow [4] proposed an effective technique which can identify the active set in a neighborhood of an isolated local solution for nonlinear programming, and Han, Jian and Li [5] improved and extended this to minimax problems. In this work, a new active constraint identification set is constructed, not only is it tighter than the previous two identification sets, but also it can be used effectively in penalty algorithms. Without strict complementarity and linear independence, it is shown that the new identification technique can accurately identify the active constraints of nonlinear programming and constrained minimax problems. Some numerical examples illustrate the identification technique.