An iterative approach to nonconvex QCQP with applications in signal processing

Abstract

Abstract-This paper introduces a new iterative approach to solve or to approximate the solutions of the nonconvex quadratically constrained quadratic programs (QCQP). First, this constrained problem is transformed to an unconstrained problem using a specialized penalty-based method. A tight upperbound for the alternative unconstrained objective is introduced. Then an efficient minimization approach to the alternative unconstrained objective is proposed and further studied. The proposed approach involves power iterations and minimization of a convex scalar function in each iteration, which are computationally fast. The important design problem of multigroup multicast beamforming is formulated as a nonconvex QCQP and solved using the proposed method.

The convex hull of a quadratic constraint over a polytope

“…A variety of complex systems can be cast as an instance of a QCQP. Combinatorial problems like MAXCUT [24], engineering problems such as signal processing [23,30], chemical process [28,40,4,19,26,55] and power engineering problems such as the optimal power flow [11,34,15,31] are just a few examples.…”