# 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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### Solution to QCQP problem and potential solvers in Python

I am working to solve a given linear system of the form $$\mathbf{A} \: \mathbf{x} = \mathbf{b}$$ where $\mathbf{x} = \begin{pmatrix} x_1 & x_2 & \cdots & x_n \end{pmatrix}^T$ with ...
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### Elementary issue with constrained optimization

I am trying to solve $$\begin{array}{ll} \text{extremize} & f(x,y) := x^2+3y\\ \text{subject to} & \dfrac{x^2}{4} + \dfrac{y^2}{9} -1 = 0\end{array}$$ I cannot understand why I am able to find ...
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### Numerically stable method to find Lagrange multipliers

Given real symmetric matrix $H$, I am trying to numerically find all critical points of the function \begin{aligned} f : \mathbb{R}^{3n} &\to \mathbb{R}\\ x &\mapsto x^T H x \end{aligned} ...
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### Reducing convex QCQP to SDP or something better

I am trying to solve the following QCQP $$\begin{array}{ll} \underset{x}{\text{minimize}} & x^T P_0 x + q_0^Tx + r_0\\ \text{subject to} & x^T P_1 x + r_1< 0\end{array}$$ where symmetric ...
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### Minimize $x^*(A+A^*)x$ such that $x^*A^*Ax=1$ and $x^*x=1$

Given $A\in\mathbb{C}^{n\times n}$, such that it has singular values larger than $1$ and smaller than $1$, \begin{array}{ll} \underset{x\in\mathbb{C^n}}{\text{minimize}} & x^*(A+A^*)x.\\ \text{...
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