In this work, we study continuous reformulations of zero-one programming problems. We prove that, under suitable conditions, the optimal solutions of a zero-one programming problem can be obtained by solving a specific continuous problem.

In this work we derive explicit descriptions for the convex envelope of nonlinear functions that are component-wise concave on a subset of the variables and convex on the other variables. These functions account for more than 30 % of all nonlinearities in common benchmark libraries. To overcome...