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.