Selecting the correct solver for minimization

Hi,

I'm trying to minimize an expression, which could look something like this: E(x,y) = sum (x_a - x_b)^2 + (y_a - y_b)^2

I guess I should use a least square solver, but how should how should I format the vector valued function? It should not output the squared error and it would be wrong to output the sum of (x_a -x_b) + (y_a - y_b). Should I instead stack the output of (x_a -x_b) and (y_a - y_b)? This will give me double the size of elements summed over. Is this problematic? Or should I use a different solver than least square solver.

The problem I'm trying to solve, is similar to estimating the Essential matrix found in Computer Vision.

Thanks in advance

Answer 1

[Alan Weiss]

I'm not sure what your decision variables are, and what variables are outside your control. Perhaps you can use lsqnonlin. http://www.mathworks.com/help/toolbox/optim/ug/lsqnonlin.html In the documentation, x represents a vector of variables that lsqnonlin can modify to search for a minimum. lsqnonlin attempts to minimuze a sum of squares of a vector function f(x).

Read the syntax carefully: lsqnonlin expects a vector function f(x), NOT a sum of squares f(1)^2 + f(2)^2 + ...

[Axel]

I'm aware of that lsqnonlin expects a vector output function. What I am asking, is what do I do, when it is not strictly a sqarred error problem.

I can't really output a single value for f(1), so I'm wondering, if I can stack two outputs for f(1) and so forth.

So my output becomes something like:

f(1)(1)

f(1)(2)

f(2)(1)

f(2)(2)

...

f(n)(1)

f(n)(2).

I tried this solution, and the error is minimized. But I am unsure if it is the correct error measure, that is minimized.

[Steve Grikschat]

It's difficult for me to follow. Can you define what f(1), f(2), etc., are? Perhaps a snippet of code would be helpful.

Also, you have a measure of error that you want to minimize (E(x,y), listed in the original post). Does that match what you get from lsqnonlin?