Optimality Conditions and Stability Analysis via the Mordukhovich Subdifferential

This article shows that finite-dimensional multiplier rules, which are based on the limiting subdifferential, can be proved by Ekeland's variational principle and some basic calculus tools of the generalized differentiation theory introduced by B. S. Mordukhovich. Consequences of a limiting constraint qualification, which yields the normal form of the multiplier rules, stability and calmness of optimization problems, are investigated in detail.