Why do I receive errors when using the LINPROG function in the Optimization Toolbox for a dense linear algebra problem?

I run the following code:

load DataFile  % you can find this file in the attachment

options = optimset(options, 'Display','iter');

X=linprog(f,[],[],Aeq,Beq,LB,UB,[],options)

I receive the following error message:

 ??? Error using ==> mtimes

 Inner matrix dimensions must agree.

 Error in ==> optim\private\lipsol>sherman at 1475

 tmp = U * (Mdense \ (U' * x));

 Error in ==> optim\private\lipsol>densol at 1422

    [x,Mdense,Rinf] = sherman(P,U,b,flag,Mdense,perm,Rinf);

 Error in ==> optim\private\lipsol at 684

       [x,Sherman_OK,Mdense,Rinf,cgiter] = ...

 Error in ==> linprog at 212

     [x,fval,lambda,exitflag,output] = 

 lipsol(f,A,B,Aeq,Beq,lb,ub,options,defaultopt,computeLambda);

Answer 1

[MathWorks Support Team]

This is a bug in the way that the LINPROG function in Optimization Toolbox handles dense columns in large scale constraint matrices.

To work around this issue, try the medium-scale simplex algorithm. Use OPTIMSET to set the "LargeScale" option to 'off' and the "Simplex" option to 'on', as shown below:

options = optimset(options, 'Display','iter','LargeScale','off','simplex','on');

X=linprog(f,[],[],Aeq,Beq,LB,UB,[],options)

To use the medium-scale algorithm involving the QPSUB function, just set the "LargeScale" option to "off":

options = optimset(options, 'Display','iter','LargeScale','off');

X=linprog(f,[],[],Aeq,Beq,LB,UB,[],options)