Suppose we have a function of the form: $(x_1 - x_2) + (x_3 - x_4) + (x_5 - x_6)$ and we have maximized this summation using linprog (using some constraints which are not important for this matter). This provides us with a value for the different x variables.
The problem I now want to solve is the maximization of the minimum $(x_i - x_j)$ and with the constraint that the solution $(x_1, x_2, ...)$ filled in in the original summation should have a higher or the same value (constraint).
This would distribute the difference between the variables $x_1,x_2; x_3,x_4, ...$
How can this problem be solved in Matlab (maximization of the minima)?