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Approximation algorithms for trilinear optimization with nonconvex constraints and its extensions

Yuning Yang (nk0310145***at***gmail.com)
Qingzhi Yang (qz-yang***at***nankai.edu.cn)

Abstract: In this paper, we study trilinear optimization problems with nonconvex constraints under some assumptions. We first consider the semidefinite relaxation (SDR) of the original problem. Then motivated by So \cite{So2010}, we reduce the problem to that of determining the $L_2$-diameters of certain convex bodies, which can be approximately solved in deterministic polynomial-time. After the relaxed problem being solved, the feasible solution of the original problem with a good approximation ratio can be obtained from the feasible solution of the relaxed problem by state-of-art algorithms. Last we consider a class of biquadratic optimization problems, which has a close relationship with the trilinear optimization problems.

Keywords: trilinear optimization, biquadratic optimization, semidefinite relaxation, approximation solution, convex bodies

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

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Entry Submitted: 04/02/2011
Entry Accepted: 04/02/2011
Entry Last Modified: 05/29/2013

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