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- Title
Algorithmic and modeling insights via volumetric comparison of polyhedral relaxations.
- Authors
Lee, Jon; Skipper, Daphne; Speakman, Emily
- Abstract
This is mostly a survey on some mathematical results concerning volumes of polytopes of interest in non-convex optimization. Our motivation is in geometrically comparing relaxations in the context of mixed-integer linear and nonlinear optimization, with the goal of gaining algorithmic and modeling insights. We consider relaxations of: fixed-charge formulations, vertex packing polytopes, boolean-quadric polytopes, and relaxations of graphs of monomials on box domains. Besides surveying the area, we do give a few new results, and we provide many directions for further work.
- Subjects
ALGORITHMS; POLYTOPES; HYPERSPACE; MATHEMATICAL optimization; INTEGERS
- Publication
Mathematical Programming, 2018, Vol 170, Issue 1, p121
- ISSN
0025-5610
- Publication type
Article
- DOI
10.1007/s10107-018-1272-6