An Eigenvalue Decomposition Method for Low-rank and Non-convex Quadratically Constrained Quadratic Programming

The quadratically constrained quadratic programming (QCQP) problems have a wide range of applications and been intensively studied in the fields of information science, control and automation engineering. Currently, one of the main challenge is to solve non-convex QCQP problem efficiently. In certain applications, the quadratic constraint coefficient matrix of QCQP problems is exactly or approximately low-rank, which can be utilized to solve the problem. In this work, we study the low-rank non-convex QCQP problems. First, a general optimization proposed. Next, we propose an eigenvalue decomposition based method to transform the low-rank non-convex quadratic constraint into a pair of linear constraints. The computational complexity is then reduced by solving a linearly constrained quadratic programming. Simulation results show that the proposed method outperforms the conventional nonlinear numerical search algorithms for QCQP in terms of optimality and computing time.