Optimization with boundaries constraints

Hello,

I am trying to solve the x that will minimize the following equation:

eq = @(x) norm(r_column-(G*x+d))^2;

Where G is 933x933, d is 933x1 and x should be 933x1, r_column is 933x1

I have the following constraints: xmin = ones(933,1)*(-30); xmax = ones(933,1)*(30);

However, if I try to solve it like this: x = fminbnd(eq,xmin,xmax);

I get an error.

I hope someone can help me, thanks in advance!

Loïc

Answer 1

[Torsten]

Try "lsqlin".

Best wishes

Torsten.

[Loic Van Aelst]

I used : x = lsqlin(-G,d-r_column,ones(2,933),[30;-30]); However the matrix x still has some values outside [-30 30]. Did I do something wrong?

Thanks for responding!

[Alan Weiss]

I am not sure that you set your bounds correctly as 933-long vectors of -30 and 30. Can you show us your real lsqlin call, based on a copy-paste from your code?

Alan Weiss

MATLAB mathematical toolbox documentation

[Loic Van Aelst]

That was a copy of my code, but I changed it to this now:

z = [eye(933) ; eye(933)]; b = [ ones(933,1)*30 ; ones(933,1)*(-30)]; x = lsqlin(-G,d-r_column,z,b);

This just gives me an x with all -30, but that problem may be due to my model.

[Torsten]

z = [eye(933) ; -eye(933)]; 
b = [ ones(933,1)*30 ; ones(933,1)*30]; 
x = lsqlin(-G,d-r_column,z,b);

Best wishes

Torsten.

[Matt J]

It is advisable to use the 7th/8th argument to express simple bounds, rather than to use inequality constraint matrices.

 e=ones(933,1)*30;

 x = lsqlin(-G,d-r_column,[],[],[],[],-e,+e);