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 et al. [F. Facchinei, A. Fischer, and C. Kanzow, On the accurate identification of active constraints, SIAM J. Optim., 9(1998), 14-32] proposed an effective technique which can identify the active set in a neighborhood of an isolated local solution for nonlinear programming. Han et al. [ D. L. Han, J. B. Jian and J. Li, On the accurate identification of active set for constrained minimax problems, Nonl. Anal.--TMA, 74(2011) 3022-3032] improved and extended it 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.
Report Jian-Group-201366, School of Mathematics and Information Science, Yulin Normal University, Yulin 537000, China, 12/2013.