For the functions, see the attachment. Minimize6.m minimizes the function
(real(b)-real(dominant2(roots(poly(x(1),x(2),x(3),x(4),x(5),x(6),x(7)))))).^2+(imag(b)-imag(dominant2(roots(poly(x(1),x(2),x(3),x(4),x(5),x(6),x(7)))))).^2
Here b is a complex number and poly(x(1),x(2),x(3),x(4),x(5),x(6),x(7))
is a polynomial of degree 7, parametrized by the seven real parameters
x(1),x(2),x(3),x(4),x(5),x(6) and x(7). Note that poly is here not
octave's build-in-function poly.m. dominant2 selects the root of the
polynomial with the biggest real part. The term should be minimized with respect to 0.5<=x(1),x(2),x(3),x(4),x(5),x(6)<=20 and 5<=x(7)<=200.
As a test case, we can take
function poly=poly(la, lb, lc, Ia, Ib, Ic, RC)
poly=[1
la+lb*RC*45*la.^7 lb+lc-RC-3*Ib*Ic Ia*RC+Ib+87*RC
Ib*Ic.^3+Ic/(Ia+Ic-la) RC-Ia*Ia*lc la*RC*Ib+Ia*RC
la-lb*lc+Ia*Ib/RC+(la.^2*lb*lc-Ia)]
minimize6.m