Georgia Institute of Technology College of Sciences

A mixed integer point is a vector in $\mathbb{R}^n$ whose first $n_1$ coordinates are integer. We present necessary and sufficient conditions for the convex hull of mixed integer points contained in a general convex set to be closed. This leads to useful results for special classes of convex sets such as pointed cones and strictly convex sets. Furthermore, by using these results, we show that there exists a polynomial time algorithm to check the closedness of the convex hull of the mixed integer points contained in the feasible region of a second order conic programming problem, for the special case this region is defined by just one Lorentz cone and one rational matrix. This is joint work with Santanu Dey.