Feasible Point Pursuit and Successive Approximation of Non-convex QCQPs

TL;DR

This paper introduces a new algorithm called FPP-SCA for solving non-convex QCQPs, which are common in signal processing and wireless communications, by efficiently finding feasible and near-optimal solutions.

Contribution

The paper proposes the FPP-SCA algorithm that adds slack variables and penalties to improve feasibility in non-convex QCQPs, ensuring convergence to KKT points.

Findings

FPP-SCA effectively finds feasible solutions where other methods fail.

The algorithm converges to KKT points when feasible.

Simulations demonstrate superior performance over existing approaches.

Abstract

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.