MIP Relaxations in Factorable Programming

Fuente: arXiv
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Main Authors: He, Taotao, Tawarmalani, Mohit
Format: Preprint
Published: 2023
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author He, Taotao
Tawarmalani, Mohit
author_facet He, Taotao
Tawarmalani, Mohit
contents 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 (MIP) 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 improves the relaxations used in a state-of-the-art solver on various instances involving polynomial functions.
format Preprint
id arxiv_https___arxiv_org_abs_2310_07168
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle MIP Relaxations in Factorable Programming
He, Taotao
Tawarmalani, Mohit
Optimization and Control
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 (MIP) 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 improves the relaxations used in a state-of-the-art solver on various instances involving polynomial functions.
title MIP Relaxations in Factorable Programming
topic Optimization and Control
url https://arxiv.org/abs/2310.07168