how to build large objective function in Optimization Toolbox?

i have an optimization problem!

GRID is a 36*400 matrix. TT is a 36*1 matrix.

my objective fuction is wrote as

function yy = GAFunction(xx)
global GRID TT 
yy = norm(GRID * xx - TT );
end

i want to solve xx using GA， fminunc，etc

when i run

GAResult = particleswarm(GAFunction,400);

or

x0 = ones(400,1);
newton = fminunc(@(x)GAFunction,x0)

it always show error

Not enough input arguments.

Error in GAFunction (line 11)
yy = norm(GRID * xx - TT );

how to build large objective function ? thank you

Answer 1

[Alan Weiss]

I don't know why you don't just use

 x = GRID\TT

but you probably have a different problem in mind that you didn't tell us.

Global variables are troublesome, I suggest that you avoid using them. Learn how to pass extra parameters using function handles or nested functions. Also, you might want to ensure that your xx variable has column orientation by changing GAFunction to use xx(:):

yy = norm(GRID * xx(:) - TT );

Alan Weiss

MATLAB mathematical toolbox documentation

[Steven Lord]

If you must use this formulation instead of backslash as Alan suggested, the cause of the error is here:

newton = fminunc(@(x)GAFunction,x0)

fminunc will call the anonymous function with one input argument and one output argument. The anonymous function will call GAFunction with zero input arguments and one output argument and will return the output it received from GAFunction as its output.

But the GAFunction needs to be called with one input argument. If you call it with zero input arguments, it doesn't know what to compute when it tries to compute GRID*xx. This is why it throws an error. In this case, you could modify the anonymous function, or use a regular function handle.

newton = fminunc(@(x)GAFunction(x),x0)
newton = fminunc(@GAFunction,x0)

[chang shu]

thank you

Alan Weiss & Steven Lord

GRID is a large sparse matrix

the result using x = GRID\TT isn't very good

so i want to try global optimization.

Matlab have serval fuctions to solve large sparse matrix , like

bicg, bicgstab

but these functions have limitations: The n-by-n coefficient matrix A must be square.

GRID is a 36*400 matrix

how can I use bicg to solve

GRID*x = TT

Regards