fminsearch used in a complex way

Hi All,

Trying to sort out a specific application of fminsearch. Here it is:

options = optimset('Display', 'off', 'Diagnostics', 'on', 'GradObj', 'off', 'TolX', 1e-6, 'TolFun',1e-6, 'MaxFunEvals', 1000);  
p = fminsearch(@(c) calc_global_angle(c, Rx*Ry, p_global), p_global, options);

And here's the calc_global_angle function:

function [residual, value] = calc_global_angle(ang, mat, p)
Rz = build_Rz(ang);
T = mat*Rz;
value = -asin(T(1,2)/sqrt(T(1,2)^2+T(2,2)^2));
residual = abs(value - p);

I can also tell you this: Rx is a 3x3 matrix. Ry is a 3x3 matrix. p_global is a scalar. p is a scalar.

And c just appears. I'm not exactly sure where the variable c comes from. It just appears, just as you see it in the p = fminsearch(...) line.

I'm also quite unclear on how you can find the minimum of a function that returns two variables (or a two element vector, if you prefer). Is it minimizing on value or residual?

Also, since the calc_global_angle takes three arguments (c, a 3x3 matrix, and another scalar), why is fminsearch returning only a scalar? Shouldn't it return the three arguments that minimize the function?

Any explanations and help that people feel like providing would be much appreciated.

Regards, Elroy

Answer 1

[Walter Roberson]

http://www.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html

[Elroy]

Walter,

That helps a great deal, but it only solves one of two problems. I now understand that c is the only input that actually changes while trying to minimize the calc_global_angle function. Or, when actually looking at the calc_global_angle, the ang argument is all that gets to change.

I'm pretty confident about all of that. However...

The calc_global_angle function returns two arguments. How would we minimize a function that returns two arguments? It's clear how to minimize a "true" function, that returns only one argument. Just keep trying until the return is as low as possible. However, with two arguments, I no longer "get" it. Are we to think of the function's return as an undulating plane, whereas we're trying to find the lowest dip in the plane?

Any clarification is truly greatly appreciated.

Elroy

[Elroy]

That's not right either. Minimizing a plane would take two inputs, and NOT two outputs. I just don't see what it means to minimize a function with two outputs.

[Walter Roberson]

http://www.mathworks.com/help/matlab/ref/fminsearch.html

fun is the function to be minimized. It accepts an input x and returns a scalar f, the objective function evaluated at x.

The second output is simply being ignored.

The first output happens to be your "residue", so basically you are searching for the angle that returns the smallest residue.

fminsearch uses a simplex type search that does not necessarily get stuck in any given local minimum, but certainly can get stuck in local minima. fminsearch() is not a global minimizer.