Probability constraints arise in many applications coming from engineering. They express that decisions have to be taken in such a way that an auxiliary inequality system, depending on the decision and a random vector, is satisfied with large enough probability. Traditional situations are ones wherein such an inequality system comes as a finite set of inequalities. There are however situations wherein such an inequality system carries infinitely many inequalities. Such a situation arises when information on uncertainty is partial: part of the distribution of the random vector is known, other components are only known to belong to some set. The latter set may actually depend on the decision vector itself, thus leading to an interesting variant of probability constraints that we shall call "probust".
In this talk, we will discuss how insights can be achieved in the understanding of (generalized) differentiation for such probust constraints.
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