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.
| Original language | English (US) |
|---|---|
| Article number | 7079378 |
| Pages (from-to) | 1623-1627 |
| Number of pages | 5 |
| Journal | IEEE Signal Processing Letters |
| Volume | 22 |
| Issue number | 10 |
| DOIs | |
| State | Published - Oct 1 2015 |
Bibliographical note
Publisher Copyright:© 1994-2012 IEEE.
Keywords
- Circulant-Toeplitz QCQP
- Toeplitz-Hermitian QCQP
- distributed spectrum sensing
- linear programming
- moving-average processes
- semi-definite relaxation
- spectral factorization