Hidden Convexity in QCQP with Toeplitz-Hermitian Quadratics

Author

Konar, Aritra ; Sidiropoulos, Nicholas D.

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN, USA

Volume

22

Issue

10

fYear

2015

fDate

Oct. 2015

Firstpage

1623

Lastpage

1627

Abstract

Quadratically Constrained Quadratic Programming (QCQP) has a broad spectrum of applications in engineering. The general QCQP problem is NP-Hard. This article considers QCQP with Toeplitz-Hermitian quadratics, and shows that it possesses hidden convexity: it can always be solved in polynomial-time via Semidefinite Relaxation followed by spectral factorization. Furthermore, if the matrices are circulant, then the QCQP can be equivalently reformulated as a linear program, which can be solved very efficiently. An application to parametric power spectrum sensing from binary measurements is included to illustrate the results.

Keywords

Hermitian matrices; Toeplitz matrices; computational complexity; linear programming; matrix decomposition; polynomials; quadratic programming; radio spectrum management; signal detection; QCQP; Toeplitz-Hermitian quadratics; hidden convexity; linear program; np-hard problem; parametric power spectrum sensing; polynomial-time; quadratically constrained quadratic programming; semidefinite relaxation; spectral factorization; Array signal processing; Covariance matrices; Linear matrix inequalities; Polynomials; Quadratic programming; Radar detection; Sensors; Circulant-Toeplitz QCQP; Toeplitz-Hermitian QCQP; distributed spectrum sensing; linear programming; moving-average processes; semi-definite relaxation; spectral factorization;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2015.2419571

Filename

7079378