Hidden Convexity in QCQP with Toeplitz-Hermitian Quadratics


Quadratically Constrained Quadratic Programming (QCQP) includes a broad spectrum of applications in engineering. The overall QCQP problem is NP-Exhausting. This text 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, that will be solved very efficiently. An application to parametric power spectrum sensing from binary measurements is included to illustrate the results.

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