# 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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### Maximum and minimum on unit circle

How would I do $f(x, y) = 5x^2 + 6y^2$ on circle $x^2+y^2 = 1$? I understand that we first solve for the critical points getting $f(0, 0) = 0$ which is the global minimum. But after that how do we ...
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### Maximize $x^2+2y^2$ subject to $y-x^2+1=0$

Maximize $x^2+2y^2$ subject to $y-x^2+1=0$ I tried using Lagrange multiplier method. We have: $$L(x,y)=x^2+2y^2+\lambda(y-x^2+1)$$ So we have: $$L_x=2x(1-\lambda)=0$$ $$L_y=4y+\lambda=0$$ One ...
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From Demidovich: Find the axes of the ellipse $5x^2 + 8xy + 5y^2 = 9$ using Lagrange multipliers. I've tried to separate into two equations, $g(x,y)$ and $f(x,y)$, to apply $$\nabla f(x,y) = -\... 0answers 41 views ### Dominant eigenvector of convex combination of Hermitian matrices Given Hermitian matrices {\bf A}, {\bf B}, {\bf C} \in \mathbb{C}^{N \times N}, we have the following optimization problem in vector {\bf x} \in \mathbb{C}^N$$\begin{array}{ll} \text{maximize} &...
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I have to solve optimization problem enter image description here How can i convert this quadratically constrained quadratic program(QCQP) into SOCP? Is this QCQP a convex problem?
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### Minimize $x y$ subject to $x^2 + y^2 \le 1$ by linear independence constraint qualification

I'm trying to solve this problem by KKT \begin{align*} \text{min} & \quad x y \\ \text{s.t} & \quad x^2 + y^2 \le 1 \end{align*} One of the regularity conditions is linear independence ...
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### Minimize $x y$ subject to $x^2 + y^2 \le 1$ by Mangasarian-Fromovitz constraint qualification

I'm trying to solve this problem by KKT \begin{align*} \text{min} & \quad x y \\ \text{s.t} & \quad x^2 + y^2 \le 1 \end{align*} One of the regularity conditions is Mangasarian-...
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### Smallest value of $x^2+5y^2+8z^2$ given $xy+yz+xz=-1$.

The question is: Find the smallest value of $x^2+5y^2+8z^2$ given $xy+yz+xz=-1$. Here's what I've tried so far. Dividing by $xyz$, I get $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{-xyz}$. ...
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### Find the minimum value of $f(x,y) = x + y^2$ given the constraint $2x^2 + y^2 = 1$

Find the minimum value of $x + y^2$ subject to the condition $2x^2 + y^2 = 1$. 1) I find $\nabla f$ and $\nabla g$ to get $$\nabla f(x,y) = (1, 2y) \\ \nabla g(x,y) = (4x, 2y)$$ Then I set up the ...
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### Maximum value of $8v_1 - 6v_2 - v_1^2 - v_2^2$ subject to $v_1^2+v_2^2\leq 1$

Given that $g:\mathbb{R}^2 \to \mathbb{R}$ defined by $$g(v_1,v_2) = 8v_1 - 6v_2 - v_1^2 - v_2^2$$ find the maximum value of $g$ subject to the constraint $v_1^2+v_2^2\leq 1.$ My attempt: Note ...
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### If $x$ and $y$ are real number such that $x^2+2xy-y^2=6$, then find the minimum value of $(x^2+y^2)^2$

If $x$ and $y$ are real number such that $x^2+2xy-y^2=6$, then find the maximum value of $(x^2+y^2)^2$ My attempt is as follows: $$(x-y)^2\ge 0$$ $$x^2+y^2\ge 2xy$$ $$2(x^2+y^2)\ge x^2+y^2+2xy$$ \...
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I am trying to implement this QCQP optimisation problem in a more efficient way. The optimisation aims to smooth an existing 3D trajectory represented by "P" which contains "n" 3D coordinates. The "n"...
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### Find Minimum + Maximum of function with constraints [closed]

homework assignment ask to find Max/Min for $$U(x,y,z) = x^2 + 2y^2 + 3z^2$$ with these constraints: $x^2 + y^2 + z^2 = 1$ $x + 2y + 3z = 0$ Thank you. First i tried to isolate x from the second ...
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