# 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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### Why is this expression the Lagrangian dual problem of this QCQP?

$\newcommand{\bx}{\mathbf{x}}$ $\newcommand{\bC}{\mathbf{C}}$ $\newcommand{\bA}{\mathbf{A}}$ $\newcommand{\bl}{\boldsymbol{\lambda}}$ $\newcommand{\bb}{\mathbf{b}}$ $\newcommand{\bQ}{\mathbf{Q}}$ ...
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### Box-constrained QCQP

Let ${\bf A} \in \mathbb{R}^{n \times n}$ be a symmetric positive semidefinite (PSD) matrix, let ${\bf a} \in \mathbb{R}^n$ and let ${\bf B} \in \mathbb{R}^{n \times n}$ be a symmetric indefinite ...
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### Maximize $x^2 + y^2$ subject to $1 \leq 2 x^2 + 4 y^2 \leq 4$
$$\begin{array}{ll} \text{maximize} & x^2 + y^2\\ \text{subject to} & 1 \leq 2 x^2 + 4 y^2 \leq 4\end{array}$$ I don't know how to apply the KKT conditions here, maybe there is other method ...