Recommendation of a minimization routine needed

[Urs Hackstein]

Dear list,

we are dealing with a minimization problem and we are looking for the
best routine in octave to solve it. Can someone recommend a good
routine for the following minimization problem?

We want to minimize the function

(p(1)-real(dominant11(roots(polyversion3(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9)))))).^2+(p(2)-imag(dominant11(roots(polyversion3(x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9)))))).^2

with respect to 0.5\leq x(1),...,x(8)\leq 20, 5\leq x(9)\leq 200 and
h\geq 0 for h=@(x)(1.85*x(1:4,1)-x(5:8,1)). We have p=[real(b),
imag(b)] for a given complex number b. Moreover polyversion3 creates a
polynomial in the variables x(1),...,x(9)
and dominant11 selects the root with the greatest real part, i.e. our
function is not continuous.

We tried to solve the problem with "sqp" which gives interesting
results, but doesn't find the best solution for some complex numbers
b.

Thus we wonder if there is a better routine to solve our minimization problem.

Thanks a lot in advance!

Best regards,

Urs Hackstein