Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/11612
Title: A tensor analogy of Yuan’s theorem of the alternative and polynomial optimization with sign structure
Authors: Hu, S
Li, G
Qi, L 
Keywords: Alternative theorem
Nonconvex polynomial optimization
Semidefinite programming
Sum-of-squares relaxation
Symmetric tensors
Issue Date: 2014
Publisher: Springer
Source: Journal of optimization theory and applications, 2014, p. 1-29 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: Yuan’s theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system involving two homogeneous quadratic functions. In this paper, we provide a tractable extension of Yuan’s theorem of the alternative to the symmetric tensor setting. As an application, we establish that the optimal value of a class of nonconvex polynomial optimization problems with suitable sign structure (or more explicitly, with essentially nonpositive coefficients) can be computed by a related convex conic programming problem, and the optimal solution of these nonconvex polynomial optimization problems can be recovered from the corresponding solution of the convex conic programming problem. Moreover, we obtain that this class of nonconvex polynomial optimization problems enjoy exact sum-of-squares relaxation, and so, can be solved via a single semidefinite programming problem.
URI: http://hdl.handle.net/10397/11612
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-014-0652-1
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