- Shown that if the feasible region is bounded, then cut generating functions for integer linear programs can easily be adapted to give the integer hull (i.e., the convex hull of the set of feasible solutions) of the conic integer program.
- Introduced a new class of cut generating functions and shown that, under some minor technical conditions, these functions, together with integer linear programming-based functions, are sufficient to yield the integer hull of intersections of conic sections in the two dimensional space.
- Generalized several well-known theoretical results in linear integer programming to the context of conic integer programming by using this new family of cut generating functions.
More details can be found in the paper:
Asteroide Santana, Santanu S. Dey. Some cut-generating functions for second-order conic sets, Discrete Optimization, 2016.