Max-min feasible point pursuit for non-convex QCQP

Abstract

Quadratically constrained quadratic programming (QCQP) has a variety of applications in signal processing, communications, and networking - but in many cases the associated QCQP is non-convex and NP-hard. In such cases, semidefinite relaxation (SDR) followed by randomization, or successive convex approximation (SCA) are typically used for approximation. SDR and SCA work with one-sided non-convex constraints, but typically fail to produce a feasible point when there are two-sided or more generally indefinite constraints. A feasible point pursuit (FPP-SCA) algorithm that combines SCA with judicious use of slack variables and a penalty term was recently proposed to obtain feasible and near-optimal solutions with high probability in these difficult cases. In this contribution, we revisit FPP- SCA from a different point of view and recast the feasibility problem in a simpler, more compact way. Simulations show that the new approach outperforms the original FPP-SCA under certain conditions, thus providing a useful addition to our non-convex QCQP toolbox.