Maximization of minimum difference

Davy

2013 5 25

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Suppose we have a function of the form: (x1 - x2) + (x3 - x4) + (x5 - x6) 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 (xi - xj) and with the constraint that the solution (x1, x2, ...) filled in in the original summation should have a higher or the same value (constraint).

This would distribute the difference between the variables x1,x2; x3,x4, ...

What function should I use for this problem (maximization of the minima)?