Questions tagged [qcqp]

A quadratically constrained quadratic program (QCQP) is an optimization problem in which both the objective function and the constraints are quadratic.

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Norm constrained least square minimization with an additional single linear equality constraint: A quadratically constrained quadratic program (QCQP)

Given is the following QCQP problem: \begin{align} &&\min_{\mathbf{x} \in \mathbb{C}^n} &\|A \mathbf{x} - \mathbf{b}\|^2,\tag{1}\label{1}\\ \text{ subject to:}&&&\\ &&\|...
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Linearisation of product of two continuous variable.

I have a quadratic constraint which I want to linearise. $x_1x_2=0$ where $0\leqslant x_1,x_2\leqslant1$. What is the best way to do this?
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Why is $\max_{c^TBc=1}c^T a a^Tc =a^TB^{-1}a$?

I'm having some trouble in understanding the last step in this sequence of equalities: $$\max_{c}\frac{c^Taa^Tc}{c^TBc}=\max_{c^TBc=1}c^T a a^Tc =a^TB^{-1}a$$ I would think that the maximum would ...
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