Guignard Qualifications and Stationary Conditions for Mathematical Programming with Nonsmooth Switching Constraints

In this paper, some constraint qualifications of the Guignard type are defined for optimization problems with continuously differentiable objec- tive functions and locally Lipschitz switching constraints. Then, a new type of stationary condition, named as parametric stationary condition, is presented for the problem, and it is shown that all the stationarity conditions in various papers can be deduced from it. This paper can be considered as an extension of a recent article (see Kanzow, et al.) to the nonsmooth case. Finally, the article ends with two important examples. The results of the article are formu- lated according to Clark subdifferential and using nonsmooth analysis methods.