Approximation algorithms for trilinear optimization with nonconvex constraints and its extensions

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 [3], we reduce the problem to that of determining the L2-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.