Approximation Bounds for Trilinear and Biquadratic Optimization Problems Over Nonconvex Constraints

Yuning Yang (), Qingzhi Yang () and Liqun Qi ()
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Yuning Yang: Nankai University
Qingzhi Yang: Nankai University
Liqun Qi: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 9, 858 pages

Abstract: 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.

Keywords: Trilinear optimization; Biquadratic optimization; Approximation bound; Convex bodies; Semidefinite relaxation; 90C26; 15A18; 15A69 (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-014-0538-2

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