New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints

In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Image: see text] -stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Image: see text] -stationarity. We show how the property of [Image: see text] -stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Image: see text] -stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Image: see text] -stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.