Eventual convexity of probability constraints with elliptical distributions

摘要: Probability constraints are often employed to intuitively define safety of given decisions in optimization problems. They simply express that a system inequalities depending on decision vector and random is satisfied with high enough probability. It known that, even if this convex the vector, associated probability constraint not general. In paper, we show some degree convexity still preserved, for large class elliptical vectors, encompassing example Gaussian or Student vectors. More precisely, our main result establishes under mild assumptions, eventual holds, i.e. when level enough. We also provide tools compute concrete certificate from nominal problem data. Our results illustrated several examples, including situation polyhedral systems technology matrices arbitrary covariance structure.