Abstract
It has been shown in a number of recent papers that Graver bases methods enable to solve linear and nonlinear integer programming problems in variable dimension in polynomial time, resulting in a variety of applications in operations research and statistics. In this article we continue this line of investigation and show that Graver bases also enable to minimize quadratic and higher degree polynomial functions which lie in suitable cones. These cones always include all separable convex polynomials and typically more.
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We thank the referees for helpful feedback which improved the presentation of this article.
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The research of Shmuel Onn was supported in part by the Loewengart Research Fund and by a grant from the Israel Science Foundation. The research of Lyubov Romanchuk was supported in part by the Technion Graduate School.
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Lee, J., Onn, S., Romanchuk, L. et al. The quadratic Graver cone, quadratic integer minimization, and extensions. Math. Program. 136, 301–323 (2012). https://doi.org/10.1007/s10107-012-0605-0
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DOI: https://doi.org/10.1007/s10107-012-0605-0
Keywords
- Integer programming
- Discrete optimization
- Graver basis
- Quadratic optimization
- Semidefinite programming
- Polynomial optimization