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# EplexInstance:piecewise_linear_hull(?X, ++Points, ?Y)

Relates X and Y according to a piecewise linear function.

X
  Parameter/domain of the piecewise function
Points
  List of points defining the piecewise function
Y
  Result/range of piecewise the function

## Description

This predicate is intended for use with hybrid ic/eplex solving. It imposes the constraint Y = f(X), where f is a piecewise linear function defined by Points: the piecewise_linear/3 constraint for the ic solver, and a linear relaxation of it for the eplex instance EplexInstance. Please see the documentation for piecewise_linear/3 for details of how the piecewise linear function is specified.

This predicate extends lib(ic)'s piecewise_linear/3 by also computing the convex hull of the portions of the constraint which are feasible with respect to the current bounds (stored with the IC bounds) of X and Y. Constraints (and bounds) defining this convex hull are then passed to the eplex instance. Changes in the IC bounds of the variables are automatically forwarded to the eplex instance, so that these constraints are updated whenever new bounds on X or Y change the convex hull. Note that the reverse, i.e. bounds changes on the eplex instance, are NOT forwarded to the IC bounds.

This implementation of the piecewise constraint accepts bounded reals in its arguments, but it does not fully support bounded reals of non-zero width (i.e. those which do not correspond to a single floating point value). As a result, use of such bounded reals is not recommended at this time.

## See Also

ic : piecewise_linear / 3