Spectral radius of asymmetric matrices


(ciel bleu) #1

hello CVXers
is there a way to calculate spectral radius of an asymmetric matrix using cvx?

Any help is appreciated,


(Mark L. Stone) #2

Have you proven this is convex?


(ciel bleu) #3

there are papers discussing Convexity and Log Convexity of the spectral radius for different cases.


(Mark L. Stone) #4

Did you carefully read the link I provided? You will have to be more specific than that.


(ciel bleu) #5

yes, i have read the link.
To be more specific :nerd_face: , suppose
spectral radius: p=| a+ib |

in my cvx code i have calculated p^2 & a^2 as scalar variables.

Question: how to add a constraint for a asymmetric matrix variable to have a spactral radius of mgnitude p and of magnitude a for its real part

Regards,


(Mark L. Stone) #6

That looks non-convex to me. Even if the spectral radius were convex, using it in an equality constraint would be non-convex.