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# min_max(?Goal, ?C, +Lower, +Upper, +Percent)

Find the solution of Goal that minimizes the maximum of elements of C, within the bounds set by Lower,Upper and Percent.

?Goal
  A callable term.
?C
  A linear term or a list of linear terms.
+Lower
  An integer.
+Upper
  An integer.
+Percent
  An integer.

## Description

If C is a linear term, a solution of the goal Goal is found that minimizes the value of C. If C is a list of linear terms, the returned solution minimizes the maximum value of terms in the list. The solution is found using the branch and bound method; as soon as a partial solution is found that is worse than a previous solution, the search is abandoned and a new solution is searched for. The starting assumption is that the value to minimize is less than Upper and that any value less than Lower can be considered as a final solution. Moreover, solutions whose minimized values are closer than Percent % are considered equal. Every time a new better solution is found, the event 280 is raised, its default handler prints the current cost.

This predicate is to be used for optimization problems when the whole search space is too large or when a suboptimal solution is sufficient.

### Fail Conditions

Fails if there is no solution to Goal.

### Resatisfiable

No.

## See Also

min_max / 2, min_max / 4, min_max / 6, min_max / 8, minimize / 2, minimize / 4, minimize / 5, minimize / 6, minimize / 8