MATLAB: Do I receive errors when using the LINPROG function in the Optimization Toolbox for a dense linear algebra problem

Optimization Toolbox

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);

Best Answer

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)
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