Abstract
Averaging has a smoothing and convexifying effect. So expectation functionals are ‘usually’ convex. However, for an important class of expectation functionals that arise in stochastic programs with chance constraints one can obtain no more than quasi-convexity. Approximation questions for this class of expectation functionals are also being considered.1
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Wets, R.JB. (1998). Stochastic Programs with Chance Constraints: Generalized Convexity and Approximation Issues. In: Crouzeix, JP., Martinez-Legaz, JE., Volle, M. (eds) Generalized Convexity, Generalized Monotonicity: Recent Results. Nonconvex Optimization and Its Applications, vol 27. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3341-8_2
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