Convexity conditions for normal mean-variance mixture distribution in joint probabilistic constraints
Résumé
In this paper, we study the linear programming with probabilistic constraints. We suppose that the distribution of the constraint rows is a normal mean-variance mixture distribution and the dependence of rows is represented by an Archimedean copula. We prove the convexity of the feasibility set in some additional conditions. Next, we propose a sequential approximation by linearization which provides a lower bound and a gradient descent method which provides an upper bound with numerical results.
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