MIP Relaxations in Factorable Programming

SIAM Journal on Optimization, Volume 34, Issue 3, Page 2856-2882, September 2024.
Abstract. In this paper, we develop new discrete relaxations for nonlinear expressions in factorable programming. We utilize specialized convexification results as well as composite relaxations to develop mixed-integer programming relaxations. Our relaxations rely on ideal formulations of convex hulls of outer-functions over a combinatorial structure that captures local inner-function structure. The resulting relaxations often require fewer variables and are tighter than currently prevalent ones. Finally, we provide computational evidence to demonstrate that our relaxations close approximately 60%–70% of the gap relative to McCormick relaxations and significantly improve the relaxations used in a state-of-the-art solver on various instances involving polynomial functions.