On a Concept of a Generic Intersection Cut Callback

Intersection cut framework can generate valid linear inequalities for a nonconvex set $S$. The framework requires a corner polyhedron relaxation of $S$, and a convex $S$-free set, which does not contain any point of $S$ in its interior. In this talk, I will review the recent development of intersection cuts in MINLPs (e.g quadratic/polynomial programming and signomial programming), featuring the construction of a variety of $S$-free sets. On the other hand, implementation of intersection cut requires much knowledge of a solver’s data structure and numerical stability. Software engineering can help here, as the solver can encapsulate cut separation procedures and provides an intersection cut callback without need for symbolic representation of $S$. Then, the users only need to provide defining-variables, zero- and first-order oracle access to the $S$-free set. I will also discuss some limitations of intersection cuts and open problems. slides

This talk is presented at session SCIP Workshop 2022 (SCIP2022).