# Questions tagged [qcqp]

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

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### How to solve a QCQP where constraints are balls?

I want to solve the following optimization problem in variables $\theta_1, \theta_2, \dots, \theta_K$ \begin{aligned} & \underset{\theta}{\text{minimize}} & & \...
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Let $P_1$, $P_2$ be two Hermitian matrices. Can anyone comment on the following QCQP? $$\begin{array}{ll} \text{minimize} & z^{H} z\\ \text{subject to} & z^{H} P_1 z +1 \leq 0\\ & z^{H} ... 1answer 375 views ### Solving a QCQP problem with sparse regularization I want to solve the follong QCQP problem:$$ \mbox{Minimize}\quad\beta^TA\beta+\mu\Omega(\beta) \mbox{s.t.}\quad\beta^TB\beta=1 \quad\mbox{and}\quad\beta\ge0  where $A$ and $B$ are both ...
I have the following quadratic optimization problem: $\min_{\vec{x}} |\vec{x}|^2$ subject to $\vec{x}^T G_j \vec{x} \geq 1$, $j = 1 \ldots m$, where the $G_j$ are positive semidefinite. $|\vec{x}|$ is ...