Re: Recommendation of a minimization routine needed

[Olaf Till]

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

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