Tagged Questions
3
votes
2answers
84 views
A standard quadratic minimization problem
Consider the "Complex" Quadratic minimization problem
\begin{align}
\min_{\mathbb{x}\in \mathbb{C}^{N \times 1}}~\mathbf{{x}}^H\mathbf{Q}\mathbf{x}-2~\Re{(\mathbf{x}^H\mathbf{b})}+1
\end{align}
...
1
vote
0answers
41 views
Minimize a complex quadratic subject to two convex quadratic constraints
I have the following the optimization problem
\begin{align}
\min_{\mathbb{x}\in \mathbb{C}^{N \times 1}}~&||\mathbb{x}^H\mathbb{u}||_2^2-2*Real\{ \mathbb{x^Hu}\}
\\\ ...
0
votes
2answers
39 views
Convexity of a function and constraint
Consider the quadratic function $f(x_1,x_2,x_3,x_4)=x_1+2x_2+4x_4+x_1^2+5x_2^2+3x_3^2x_4^2-4x_1x_2-2x_2x_3+2x_3x_4$. Is f a convex function?
Consider a constraint defined using the above function f: ...
3
votes
1answer
120 views
Why does positive semi-definiteness in this inequality imply a convex set?
I was reading a proof that rewrote an inequality in the form:
$$b^Tx +x^T A x \le \alpha$$
for $b,x \in \mathbb{R}^n$ and $\alpha \in \mathbb{R}$, and with $A$ positive semidefinite. It then ...
0
votes
1answer
96 views
General quadratic form of two variables
I was referring to this lecture http://www.stanford.edu/class/ee364a/videos/video04.html. and he gave an example of a generalized quadratic equation
...
