Cut separation via facial reduction and lifting

Abstract

We present a new procedure for separating split cuts in mixed-integer conic programming. A cut is obtained by identifying a valid inequality for a facial restriction of the problem, which is then lifted to the original space. This technique is applicable when the point to separate lies at the boundary of its conic domain, and corresponds to applying a facial reduction to the corresponding membership problem. In doing so, we reduce the size of the separation and, at best, reduce it to an LP.

Mathieu Tanneau

Research Engineer

I’m interested in mixed-integer linear and nonlinear optimization, power systems, and the integration of machine-learning techniques in optimization algorithms.