Scaling LMI inequalities

I am working in structural optimization (primarily truss and cable structures) and I notice that scaling of LMI improves convergence a lot

(Qred * diag(A/Ascaling) * Qred’- omega2base*(diag(Jred * A/Ascaling) + M0))/Kmax == semidefinite(nfree)


(Qred * diag(A) * Qred’- omega2base * (diag(Jred * A) + M0))== semidefinite(nfree)

“A” is the main variable (cross-sectional area of truss of order 1e-4 m^2). “Ascaling” scales “A” to order 1. “Kmax” is 0.1 norm (Qreddiag(Aref)*Qred’) and it can be for steel structures of order 10^7 or 10^8. “Kmax” scales the coefficients in LMI to a range from 0.1 to 10.

Is there a systematic reference on how to do it properly?

You can look at .

Thanks, that is a great link!