Re: Optimization in Octave

[Julien Bect]

On 12/03/2014 16:03, Urs Hackstein wrote:
> Dear Julien, thanks a lot for your detailed explanations. I just 
> started to check them. F->-F doesn't work better. A better starting 
> point improves the result, but I don't know how to choose the 
> appropriate starting point. I assumed that our problem has local 
> optima, but I can't prove it.

Then let's assume that your problem has local optima => you need 
something "less local" than sqp.

The simplest than you can do is use a "random start" approach : use a 
local solver (e.g., sqp) repeatedly from random starting points.

This is very easy to implement with a for loop around the code that you 
already have written :

x_opt = [];
obj_opt = Inf;

n_try = 100;

for i = 1:n_try,

    lbound = [0.5,0.5,0.5,0.5,5]';
    ubound = [20,20,20,20,200]';
    x_init = lbound + (lbound - ubound) .* rand (5, 1);

    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, obj] = sqp(x_init,F,G,h,lbound,ubound,500)

    if obj < obj_opt,
        x_opt = x;
        obj_opt = obj
    endif

endfor

If your problem is very difficult you might have to increase n_try, of 
course.