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Croatian Operational Research Review, Vol. 5 No. 2, 2014.
Izvorni znanstveni članak
https://doi.org/10.17535/crorr.2014.0001
From combinatorial optimization to real algebraic geometry and back
Janez Povh
; Faculty of Information Studies Novo Mesto
| Puni tekst: engleski, pdf (113 KB) | str. 105-117 | citiraj | |
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APA 6th Edition Povh, J. (2014). From combinatorial optimization to real algebraic geometry and back. Croatian Operational Research Review, 5 (2), 105-117. https://doi.org/10.17535/crorr.2014.0001 MLA 8th Edition Povh, Janez. "From combinatorial optimization to real algebraic geometry and back." Croatian Operational Research Review, vol. 5, br. 2, 2014, str. 105-117. https://doi.org/10.17535/crorr.2014.0001. Citirano 21.02.2019. Chicago 17th Edition Povh, Janez. "From combinatorial optimization to real algebraic geometry and back." Croatian Operational Research Review 5, br. 2 (2014): 105-117. https://doi.org/10.17535/crorr.2014.0001 Harvard Povh, J. (2014). 'From combinatorial optimization to real algebraic geometry and back', Croatian Operational Research Review, 5(2), str. 105-117. doi: https://doi.org/10.17535/crorr.2014.0001 Vancouver Povh J. From combinatorial optimization to real algebraic geometry and back. Croatian Operational Research Review [Internet]. 2014 [pristupljeno 21.02.2019.];5(2):105-117. doi: https://doi.org/10.17535/crorr.2014.0001 IEEE J. Povh, "From combinatorial optimization to real algebraic geometry and back", Croatian Operational Research Review, vol.5, br. 2, str. 105-117, 2014. [Online]. doi: https://doi.org/10.17535/crorr.2014.0001 |
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Sažetak
In this paper, we explain the relations between combinatorial optimization and real algebraic geometry with a special focus to the quadratic assignment problem. We demonstrate how to write a quadratic optimization problem over discrete feasible set as a linear optimization problem over the cone of completely positive matrices. The latter formulation enables a hierarchy of approximations which rely on results from polynomial optimization, a sub- eld of real algebraic geometry.
Ključne riječi
combinatorial optimization; copositive programming; semide nite programming; polynomial optimization; sum of squares; real algebraic geometry
Hrčak ID: 133615
URI
https://hrcak.srce.hr/133615
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