Re: Recommendation of a minimization routine needed

[Urs Hackstein]

2014-02-06, Olaf Till <address@hidden>:
> On Thu, Feb 06, 2014 at 01:40:16PM +0100, Urs Hackstein wrote:
>> 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.
>
> Maybe a stochastic optimizer? In package 'optim', function
> 'nonlin_min', backend 'siman' does simulated annealing and honours
> constraints. If you set the option 'stoch_regain_constr' to true, it
> should be advisable to formulate your constraint 'h' as a linear
> constraint according to the syntax of the function interface, since
> regaining the constraint will be more easy for the backend in this
> case.
>
> This backend is only little tested.
>
> Olaf
>
> --
> public key id EAFE0591, e.g. on x-hkp://pool.sks-keyservers.net
>


Dear Olaf,

thanks a lot for your tip which sounds interesting to me.

Unfortunately, I couldn't find an example how to use package optim,
function nonlin_min, backend samin. (There is none under "help
nonlin_min" and I only found an example for package optim, function
samin - which seems to be something different.) Thus could you please
provide an easy example?

Best regards,

Urs