Approximation Bounds for Trilinear and Biquadratic Optimization Problems Over Nonconvex Constraints |
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Authors: | Yuning Yang Qingzhi Yang Liqun Qi |
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Institution: | 1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin?, 300071, People’s Republic of China 2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, People’s Republic of China
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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. |
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