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Gamma uncertainty sets have been introduced for adjusting the degree ofconservatism of robust counterparts of (discrete) linear programs. Thecontribution of this paper is a generalization of this approach to (mixedinteger) nonlinear optimization programs. We focus on the cases in which theuncertainty is linear or concave but also derive formulations for the generalcase. By applying reformulation techniques that have been established fornonlinear inequalities under uncertainty, we derive equivalent formulations ofthe robust counterpart that are not subject to uncertainty. The computationaltractability depends on the structure of the functions under uncertainty andthe geometry of its uncertainty set. We present cases where the robustcounterpart of a nonlinear combinatorial program is solvable with a polynomialnumber of oracle calls for the underlying nominal program. Furthermore, wepresent robust counterparts for practical examples, namely for (discrete)linear, quadratic and piecewise linear settings. Keywords: Budget Uncertainty,Discrete Optimization, Combinatorial Optimization,

Gamma counterparts for robust nonlinear combinatorial and discrete optimization