  Quadratically constrained quadratic programs (QCQPs) have a wide range of
applications in signal processing and wireless communications. Non-convex QCQPs
are NP-hard in general. Existing approaches relax the non-convexity using
semi-definite relaxation (SDR) or linearize the non-convex part and solve the
resulting convex problem. However, these techniques are seldom successful in
even obtaining a feasible solution when the QCQP matrices are indefinite. In
this paper, a new feasible point pursuit successive convex approximation
(FPP-SCA) algorithm is proposed for non-convex QCQPs. FPP-SCA linearizes the
non-convex parts of the problem as conventional SCA does, but adds slack
variables to sustain feasibility, and a penalty to ensure slacks are sparingly
used. When FPP-SCA is successful in identifying a feasible point of the
non-convex QCQP, convergence to a Karush-Kuhn-Tucker (KKT) point is thereafter
ensured. Simulations show the effectiveness of our proposed algorithm in
obtaining feasible and near-optimal solutions, significantly outperforming
existing approaches.
