Re: Optimization in Octave

[Julien Bect]

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
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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 or NLopt.

@++
Julien