Easy distributions for combinatorial optimization problems with probabilistic constraints
Operations Research Letters
Uniform quasi-concavity in probabilistic constrained stochastic programming
Operations Research Letters
A second-order cone programming approximation to joint chance-constrained linear programs
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Safe Approximations of Ambiguous Chance Constraints Using Historical Data
INFORMS Journal on Computing
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We investigate the convexity of chance constraints with independent random variables. It will be shown, how concavity properties of the mapping related to the decision vector have to be combined with a suitable property of decrease for the marginal densities in order to arrive at convexity of the feasible set for large enough probability levels. It turns out that the required decrease can be verified for most prominent density functions. The results are applied then, to derive convexity of linear chance constraints with normally distributed stochastic coefficients when assuming independence of the rows of the coefficient matrix.