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Title: Approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints
Authors: Yang, Y
Yang, Q
Qi, L 
Keywords: Approximation bound
Biquadratic optimization
Convex bodies
Semidefinite relaxation
Trilinear optimization
Issue Date: 2014
Publisher: Springer
Source: Journal of optimization theory and applications, 2014, p. 1-18 How to cite?
Journal: Journal of optimization theory and applications 
Abstract: This paper presents new approximation bounds for trilinear and biquadratic optimization problems over nonconvex constraints. We first consider the partial semidefinite relaxation of the original problem, and show that there is a bounded approximation solution to it. This will be achieved by determining the diameters of certain convex bodies. We then show that there is also a bounded approximation solution to the original problem via extracting the approximation solution of its semidefinite relaxation. Under some conditions, the approximation bounds obtained in this paper improve those in the literature.
ISSN: 0022-3239
EISSN: 1573-2878
DOI: 10.1007/s10957-014-0538-2
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