# 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{equation} \begin{aligned} & \underset{\theta}{\text{minimize}} & & \...
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### Solving a non-convex quadratically-constrained quadratic program

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 ...
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### Complexity of convex quadratically constrained quadratic programming (QCQP)

Could someone tell me the time complexity of a convex quadratically constrained quadratic program (QCQP)? Any references?