# Questions tagged [qclp]

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

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### Convex optimization problem with quadratic constraint [closed]

$$\min_{x} c^Tx$$ such that $$||Ax||^2_2 \le 1$$ where $$A \succ 0$$ I feel like this should be easy but I have been struggling for hours. Is this a second-order cone constraint? How do I begin to ...
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### Constrained convex optimization [duplicate]

Solve Maximize $f(x)=c^Tx$ subject to $x^TQx \leq 1$ where $Q$ is a positive definite matrix. what is the solution if the objective function is to be minimized ?
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### Minimize with Lagrange multiplier

$$\begin{array}{ll} \text{minimize} & f(x,y,z) := x+2y+z\\ \text{subject to} & g(x,y,z) := x^2+y^2+z^2-1=0\end{array}$$ I get the following $\nabla f=(1,2,1)$ and $\nabla g=(2x,2y,2z)$. Now, ...
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### Minimize $x + z$ subject to $x^2 + y^2 = 1$ and $y^2+z^2 = 4$

I'm trying to solve this problem by KKT's condition: \begin{align*} \text{min} & \quad x + z \\ \text{s.t} & \quad x^2 + y^2 = 1 \\ & \quad y^2+z^2 = 4 \end{align*} One ...
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### Minimise $2x+y$ subject to $x^2+y^2=1$ using KKT

I'm doing this exercise in preparing for the final exam in optimization: \begin{align*} \text{min} &\quad 2x+y \\ \text{s.t} & \quad x^2+y^2=1 \end{align*} Could you please verify if I ...
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1 vote
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### How to solve this convex optimization problem (with absolute and linear objective function)?

I have the following problem: \begin{align*} \sup_y&\quad \big | \langle u,y \rangle\big |\\ \mbox{s.t.}&\quad \frac{1}{2}\langle y,y \rangle\ + \langle b,y \rangle\ \geq \gamma. \end{align*...
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The context is ordinary multivariate regression with $k$ (>1) regressors, i.e. $Y = X\beta + \epsilon$, where $Y \in \mathbb{R}^{n \times 1}$ vector of predicted variable, \$X \in \mathbb{R}^{n \times (...