Hi there,
I have a question to the community: I would like to use the function f(x, y) = \frac{y}{2}(\frac{x}{y} -c)^2 for scalar variables x and y>0 and a constant c. This function is convex, however it is not recognized as such by cvx. I have been scanning through the available cvx functions but none seemed to be suitable.
Does anybody have an idea for a workaround?
Thx for any help!
You have
f(x,y) = 0.5 (\frac{x^2}{y} + c^2 y - 2 c x)
Maybe CVX understand that. Otherwise using a rotated quadratic cone it can easily be made DCP compliant:
\begin{array}{rcl}
f(x,y) &=& 0.5 (2 z+ c^2 y - 2 c x) \\
2 z y & \geq &x^2 \\
z,y & \geq & 0
\end{array}
Last two inequalities are a rotated quadratic cone.
Thank you. The function quad_over_lin(x,y) does the job for the first solution.
Yes of course.
CVX converts to the form I mentioned at its backend I suppose.
