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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2013, Volume 53, Number 5, Pages 816–824
DOI: https://doi.org/10.7868/S0044466913050165 (Mi zvmmf9862) 		 
Cones of multipowers and combinatorial optimization problems

M. N. Vyalyi

Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow
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DOI: https://doi.org/10.7868/S0044466913050165
Abstract: The cone of multipowers is dual to the cone of nonnegative polynomials. The relation of the former cone to combinatorial optimization problems is examined. Tensor extensions of polyhedra of combinatorial optimization problems are used for this purpose. The polyhedron of the MAX-2-CSP problem (optimization version of the two-variable constraint satisfaction problem) of tensor degree $4k$ is shown to be the intersection of the cone of $4k$-multipowers and a suitable affine space. Thus, in contrast to SDP relaxations, the relaxation to a cone of multipowers becomes tight even for an extension of degree 4.
Key words: combinatorial optimization problems, cones of multipowers, tensor extensions of polyhedra.
Received: 29.11.2012
English version:
Computational Mathematics and Mathematical Physics, 2013, Volume 53, Issue 5, Pages 647–654
DOI: https://doi.org/10.1134/S096554251305014X
Bibliographic databases:
Document Type: Article
UDC: 519.67
Language: Russian
Citation: M. N. Vyalyi, “Cones of multipowers and combinatorial optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 53:5 (2013), 816–824; Comput. Math. Math. Phys., 53:5 (2013), 647–654
Citation in format AMSBIB
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