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)?

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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)?

anclarlo5h12v · Accepted Answer

In order to maximize a minimum using linear programming techniques, you can introduce an additional variable   δ and add constraints of the form      x    i    −      x    j    ≥  δThe variable   δ must then be maximized. For your problem to be well-defined there should of course be additional constraints on the variables       x    i  , probably like the ones you used in the first problem.

Suppose we have a function of the form: ( x 1 </msub> −

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