Convexity of chance constrained programming problems with respect to a new generalized concavity notion

In this paper, convexity of chance constrained problems have been investigated. A new generalization of convexity concept, named h-concavity, has been introduced and it has been shown that this new concept is the generalization of the α-concavity. Then, using the new concept, some of the previous results obtained by Shapiro et al. [in Lecture Notes on Stochastic Programming Modeling and Theory, SIAM and MPS, 2009] on properties of α-concave functions, have been extended. Next the convexity of chance constraints with independent random variables is investigated. It will be shown how concavity properties of the mapping related to the decision vector have to be combined with suitable properties of decrease or increase for the marginal densities in order to arrive at convexity of the feasible set for large enough probability levels and then sufficient conditions for convexity of chance constrained problems which has been introduced by Henrion and Strugarek [in Convexity of chance constraints with independent random variables. Comput. Optim. Appl. 41:263–276, 2008] has been extended in this paper for a wider class of real functions.