On solving biquadratic optimization via semidefinite relaxation

In this paper, we study a class of biquadratic optimization problems. We first relax the original problem to its semidefinite programming (SDP) problem and discuss the approximation ratio between them. Under some conditions, we show that the relaxed problem is tight. Then we consider how to approximately solve the problems in polynomial time. Under several different constraints, we present variational approaches for solving them and give provable estimation for the approximation solutions. Some numerical results are reported at the end of this paper.