Re: Optimization in Octave

[Urs Hackstein]

2014-02-28 13:55 GMT+01:00, Julien Bect <address@hidden>:
> On 28/02/2014 12:07, Juan Pablo Carbajal wrote:
>> On Fri, Feb 28, 2014 at 11:45 AM, Urs Hackstein
>> <address@hidden> wrote:
>>> Dear all,
>>>
>>> we have the following optimization problem: Given a (nonlinear, but
>>> almost everywhere differentiable) function
>>>
>>> p:[0.5,20]^4*[5,200]\to\mathbb{C}
>>>
>>> we want to find the maximum of
>>>
>>> Re(p(x_1,x_2,x_3,x_4,x_5))
>>>
>>> for fixed imaginary part
>>> Im(p(x_1,x_2,x_3,x_4,x_5))=y_0.
>>> Is it possible to solve this problem using Octave?
>>> Thanks a lot in advance!
>>>
>>> Best regards,
>>>
>>> Urs Hackstein
>>> _______________________________________________
>>> Help-octave mailing list
>>> address@hidden
>>> https://mailman.cae.wisc.edu/listinfo/help-octave
>> If you have the function, and you want to fix the imaginary part, then
>> you have a real function. If it is differentiable, I see no problem
>> using gradient based methods. If it is not differentiable then you can
>> use ga, or in prticular cma-es
>> https://www.lri.fr/~hansen/cmaes_inmatlab.html
>
> I would rather say that this is an *equality constrained* problem with 5
> variables and 1 equality constraint.
>
> In Octave core, you can try sqp to solve it. Something like :
>
>      F = @(x)(real (p (x(1), x(2), x(3), x(4), x(5)));
>      G = @(x)(imag (p (x(1), x(2), x(3), x(4), x(5)) - y_0);
>
>      lb = [0.5 0.5 0.5 0.5 5];
>      ub = [20 20 20 20 200];
>
>      x_opt = sqp (x_init, F, G, [], lb, ub)
>
> Type "help sqp" for more details. You can also provide the gradient, if
> you have it.
>
> If sqp doesn't work for you, have a look at the optim package
> <http://octave.sourceforge.net/optim/index.html> or NLopt
> <http://ab-initio.mit.edu/wiki/index.php/NLopt>.
>
> @++
> Julien
>
>

Dear Julien,

thanks a lot for your explanations. I tried to formulate my problem as
a function with variable y_0 using sqp in the meantime, but I receive
still an error that I don't understand.

My attempt was the following:

function x_opt=opt(b)

x_init = 5*ones(5,1);
lbound = [0.5,0.5,0.5,0.5,5]';
ubound = [20,20,20,20,200]';
F=@(x)(real(p(x(1),x(2),x(3),x(4),x(5))));
G=@(x)(imag(p(x(1),x(2),x(3),x(4),x(5)))-b);
h=@(x) (1.85.*x(1:2,1) - x(3:4,1))
x_opt=sqp(x_init,F,G,h,lbound,ubound,500)

and the error is

error: qp: equality constraint matrix must be full row rank
error: called from:
error:   /usr/local/share/octave/3.6.4/m/optimization/qp.m at line
325, column 11
error:   /usr/local/share/octave/3.6.4/m/optimization/sqp.m at line
414, column 32
error:   /home/hackstein/............./opt.m at line 11, column 6

What am I missing?

Thanks a lot in advance.

Best regards,

Urs Hackstein