How should I manage the input on fmincon function?

Hi there,

I am using the fmincon function in order to minimize an image registration problem.

After preprocessing and several Gaussian reductions I obtain two data volumes/matrix (100,100,400 every one).

To optimize the result, every slice of the matrix can be moved in three axis (x, y, z). So, I need a 3(x,y,z)x400=1200 variables for every volume as initial guess. I pass them as a vector, InitialVector. The data volumes are passed as global variables. I am using the limited memory BFGS.

My problem is with respect the A and b variables of input.

How should I configure them? What size?

options = optimset('Algorithm','interior-point','Hessian',{'lbfgs',1000}); [FinalValue,fval,exitflag,output]=fmincon(@Optimizer,InitialVector,A,b,[],[],[],[],[],options);

Any suggestion will be truly appreciated!

Answer 1

[Shashank Prasanna]

A and b are linear constraints, if you don't have any linear constraints just use empty brackets. If you do then see the doc on how to phrase them. A has coefficients for the linear combination of x to be less than b:

http://www.mathworks.com/help/optim/ug/fmincon.html#f844862

Also I'd advise against global variables and passing extra parameters through anonymous variables as follows:

http://www.mathworks.com/help/optim/ug/passing-extra-parameters.html#brhkghv-9

Answer 2

[Michael]

Thanks for the answer.

If I use empty brackets for A,b appears the following problem:

Error using fmincon (line 218) FMINCON is for constrained problems. Use FMINUNC for unconstrained problems.

the matter is I need use the Limited Memory Broyden-Fletcher-Goldfarb-Shannon (LBFGS).

Is there any way to use this method (LBFGS) with the FMINUNC funtion?

About the global variables, I dont think so it is possible to pass them as extra parameters. My funtion is like this:

MAIN Function ...

options = optimset('Algorithm','interior-point','Hessian',{'lbfgs',1000}); [FinalValue,fval,exitflag,output]=fmincon(@Optimizer,InitialVector,A,b,[],[],[],[],[],options);

My fun

function [FinalValue]=Optimizer(InitialVector)

[BScanCubeX BScanCubeY]=VectorDisplacement(InitialVector); FinalValue=IterativeMeritFunction(BScanCubeX,BScanCubeY);

end

In VectorDisplacement funtion there are (with every iteration) changes in the position of the voxels in order to minimize the subtraction between BScanCubeX and BScanCubeY data sets.

    NumberKX=InitialVector(1,:);
    NumberKY=InitialVector(2,:);

    IndexX=find(NumberKX>0);
    IndexY=find(NumberKY>0);
    NumberImagX=length(IndexX);
    NumberImagY=length(IndexY);

    NumberImag=NumberImagX+NumberImagY;

    for k=1:NumberImag        %%Positive Displacement Counter

        if NumberImagY-k>=0                BScanCubeYY(:,IndexY(k)),:)=zeros(DimensionsVector(2,3,2),DimensionsVector(3,3,2));         BScanCubeYY(1:DimensionsVector(1,3,2)-(NumberKY(IndexY(k)))+1,IndexY(k),:)=CY3(NumberKY(IndexY(k)):DimensionsVector(1,3,2),IndexY(k),:); %
        end

        if NumberImagX-k>=0
          BScanCubeXX(IndexX(k),:,:)=zeros(DimensionsVector(2,3,1),DimensionsVector(3,3,1));          BScanCubeXX(IndexX(k),1:DimensionsVector(2,3,1)-(NumberKX(IndexX(k)))+1,:)=CX3(IndexX(k),NumberKX(IndexX(k)):DimensionsVector(2,3,1),:);

        end

So, any help, please?