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Given a finite ground set N and a value vector a ∈ R N , we consider optimization problems involving maximization of a submodular set utility function of the form h(S) = f i∈S a i , S ⊆ N , where f is a strictly concave, increasing, differentiable function. This utility function appears frequently in combinatorial optimization problems when modeling risk aversion and decreasing marginal preferences, for instance, in risk-averse capital budgeting under uncertainty, competitive facility location,doi:10.1007/s10107-009-0298-1 fatcat:kisqitzwm5h65l5v5keyc3m55y