How to use fminsearch with several parameters in the right way?

Hello,

it is the first time that I try use some optimization and somebody told me it is a good idea to use fminsearch?

Aim:

I got a function sumDist = transDist(feat1, feat2, tP) and I want to optimize it:

y = fminsearch (@(x) transDist(this.featP1, this.featP2, x), 0);

0 would be the optimal result of the function but it is like unreachable. x is an vector of size 9 where value 4 to 6 are angles in radians, don't know if i need to limit the value range and how i could do this. As result i would like to get the x vector for the best result fminsearch was able to find.

I hope you can help me a little bit with that.

Thank you in advance.

Greetings,

me

@Edit1 (2016-07-08 08:17:00) fminsearch should be fine but 1 thing I noticed in the first comment is

x0 = zeros(9,1);

but I don't know what a good value for the input could be. I only know that 0 as a result would be the best possible solution for the output. My function calculates a scaling, rotation, transformation in 3D until featP1 fit best to featP2. Could you help me solve this problem, because if this doesn't work I got no Idea how to make it work.

[jgg]

It sounds like the issue is that you have a constraint optimization problem, not an unconstrained problem. fminsearch is an unconstrained solver; it doesn't know that elements 4,5,6 of your vector are radians and so is probably finding some erroneous solution.

As a built in, your best alternative is probably fmincon which has constraints. You likely just want to set the lb ub parameters:

 lb = ones(9,1)*-Inf;
 ub = ones(9,1)*Inf; 
 lb(4) = 0; ub(4) = 2*Pi;
 lb(5) = 0; ub(5) = 2*Pi;
 lb(6) = 0; ub(6) = 2*Pi;

Then just pass them in, along with anything else you want:

 fun = @(x)transDist(this.featP1, this.featP2, x);
 x0 = zeros(9,1);
 x = fmincon(fun,x0,[],[],[],[],lb,ub)

[John D'Errico]

You really don't care if those parameters are angular, as they have no boundaries. 2*pi+k is the same angle as k.

So there is no need to apply bounds to those numbers. If having an angle that is greater than 2*pi bothers you, then use

mod(x,2*pi)

after the solver is done to map your angles into the interval [0,2*pi).

As far as needing to use a bounded solver to apply bounds, you can use my fminsearchbnd from the file exchange. It has the capability to apply bounds when using a fminsearch tool. 9 variables is near (or even beyond) the upper limits that I usually suggest is a good idea for those schemes. But it will probably work, just taking longer than I would like.

[jgg]

Doesn't that mechanically mean that you're going to find multiple solutions to his optimization problem? This seems like a bad idea, since most solvers use some kind of gradient descent which will get confused if there's more than one optimum near them.

[Walter Roberson]

fminsearch does not get "confused" by multiple identical optimum: it just randomly ends up in one of the basins.

[Walter Roberson]

If you have no idea what a good starting point is, then you might as well pick a value at random out of the entire range of values possible for that position. For example,

RR = @(A,B) A + rand()*(B-A);
x0 = [RR(-500,750), RR(0, realmax), RR(-pi,pi), RR(-pi,pi), RR(-pi,pi)];

This would construct a vector in which the first element was chosen uniform randomly over (-500,750), the second over (0, 1E+308), and the other three over -pi to +pi.

And then if you don't get a nice result, you can randomly generate again...

Answer 1

[baxbear]

x0 = zeros(9,1);

and

x0 = rand(9, 1);

are the best ways to use my matlab function, 0 does not work because then fminsearch does not know that I am looking for a vector of size 9.

[Marc]

This is not an "accepted" answer to the question. Nobody knows what you are looking for because your question was pretty vague. There are well known reasons why a Nelder Mead Simplex approach works and doesn't work. There is also a good reason why The Mathworks Co. sells an Optimaztion and Global Optimaztion toolbox.

[Walter Roberson]

The poster Accepted their own Answer, so it was an answer that served their purpose. (It was pretty much the answer the volunteers had described.)