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In this paper, we study cut generating functions for conic sets. Our firstmain result shows that if the conic set is bounded, then cut generatingfunctions for integer linear programs can easily be adapted to give the integerhull of the conic integer program. Then we introduce a new class of cutgenerating functions which are non-decreasing with respect to second-ordercone. We show that, under some minor technical conditions, these functionstogether with integer linear programming-based functions are sufficient toyield the integer hull of intersections of conic sections in $\mathbb{R}^2$.

Some cut-generating functions for second-order conic sets