How to define Linear program in matlab?

Question

I'm having trouble defining my optimization problem in MATLAB.

I'm trying to express 7 binary decision variables. but the sum of the first 3 binary decsion varibles cannot be greater than1, and the sum of the last 4 binary decision variables cannot be greater than 1.

A = [1,1,1,0,0,0,0;...
    0,0,0,1,1,1,1];
b = [1;1];

% objective function 
f = [0.1, 0.5, 0.2, 0.2, -2.0, 0.2, 0.6];

lb = zeros(7,1);
ub = ones(7,1); % Enforce all of the decision variables to be binary
intcon = [];  % all of my variables are binary, so I assume this should be blank.

x = intlinprog(f,intcon,A,b,lb,ub);

I want to Enforce all of the decision variables to be binary, so I included these lines:

lb = zeros(7,1);
ub = ones(7,1); % Enforce all of the decision variables to be binary 
intcon = [];  % all of my variables are binary, so I assume this should be blank.

Also, I have no equality constraints, so I did not include Aeq and beq in the problem above. but when I try to run the solver without those parameters likex = intlinprog(f,intcon,A,b,lb,ub); it tells me

Error using intlinprog (line 123)
The number of columns in Aeq must be the same as the number of elements of f.

But if I do not have any equality constraints, how am I supposed to define this?

Here is the documentation: https://www.mathworks.com/help/optim/ug/intlinprog.html#bts3gkc-2 The example at the top of the page shows that it can call x = intlinprog(f,intcon,A,b) without using Aeq and beq, so I know it is possible.

thanks.

You might want to fix your description, since what you have is not a linear program. And if all your variables are binary, then they all need to be listed in the integer constraint. Otherwise it will optimize a linear program, where each of the variables takes on any real value on the closed interval [0, 1]. — Ben Voigt
– Ben Voigt, Commented Mar 12, 2018 at 2:15

Ben Voigt · Accepted Answer · 2018-03-12 02:16:35Z

1

You cannot omit Aeq and Beq if you specify the lower-bound and upper-bound constraints, because this function uses positional parameters.

However, you can pass empty matrices, resulting in zero equality constraints:

x = intlinprog(f,intcon,A,b,[],[],lb,ub);

answered Mar 12, 2018 at 2:16

Ben Voigt

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