We introduce a constraint qualification condition (GPMFCQ) for smooth infinite programming problems, where the nonlinear operator defining the equality constraints has nonsurjective derivative at the local minimum. The condition is a generalization of PMFCQ introduced by Morduhovich and Nghia. We prove the existence of Lagrange multipliers by using either Hurwicz set or Nonlinear Farkas Minkowski condition.
@article{arxiv.2412.19642,
title = {Mangasarian-Fromovitz-type constraint qualification and optimality conditions for smooth infinite programming problems},
author = {Ewa M. Bednarczuk and Krzysztof W. Leśniewski and Krzysztof E. Rutkowski},
journal= {arXiv preprint arXiv:2412.19642},
year = {2024}
}