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Consider a set of $A_{vn}$ decision variables such that $A_{v1},A_{v2},\cdots,A_{vn}<A$. While this is the standard formulation finding the maximum value of $A_{vn}$, I would also like to find the second largest $A_{vn}$ of this set of decision variables.

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    $\begingroup$ Are the $n$ values known to be distinct? If not, what is the desired behavior if there is a tie for largest? $\endgroup$ – RobPratt Sep 9 at 3:46
  • $\begingroup$ Yes and no unfortunately, of all of them, only either one or two of them are to be non-zero, i.e., the others are to be zero. Additionally, all of them are integers that are to be greater or equal to zero. Lastly, the two non-zero variables might also be equal, though they should be unequal most of the time. Sorry for the initial omission of such information. Thank you! $\endgroup$ – Mike Sep 9 at 3:54
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    $\begingroup$ Then just take the sum of all of them and subtract the largest. $\endgroup$ – RobPratt Sep 9 at 4:00
  • $\begingroup$ Dear Dr Rob, Thank you very much! $\endgroup$ – Mike Sep 9 at 6:35
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To get the second largest variable when all are nonnegative and at most two can be nonzero, just take the sum of all of them and subtract the largest.

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