ILOG CPLEX C++ API 9.0 Reference Manual

IloCplex::VariableSelect
Group optim.cplex.cpp.piecewiselinear
The API of ILOG CPLEX Piecewise Linear Formulations for users of C++.
IloCplex::PWLFormulation
Enumerations Summary
Description
Piecewise Linearity in ILOG CPLEX
Some problems are most naturally represented by constraints over functions that are
not purely linear but consist of linear segments. Such functions are sometimes known
as piecewise linear.
How to Define a Piecewise Linear Function
To define a piecewise linear function in Concert Technology, you need these
components:
◆ the variable of the piecewise linear function;
◆ the breakpoints of the piecewise linear function;
◆ the slope of each segment (that is, the rate of increase or decrease of the function
between two breakpoints);
◆ the geometric coordinates of at least one point of the function.
In other words, for a piecewise linear function of n breakpoints, you need to know n+1
slopes. Typically, the breakpoints of a piecewise linear function are specified as an
array of numeric values. The slopes of its segments are indicated as an array of
numeric values as well. The geometric coordinates of at least one point of the function
must also be specified. Then in Concert Technology, those details are brought together
in an instance of the class IloPiecewiseLinear.
Another way to specify a piecewise linear function is to give the slope of the first
segment, two arrays for the coordinates of the breakpoints, and the slope of the last
segment.
For examples of these ways of defining a piecewise linear function, see this topic in the
ILOG CPLEX User's Manual.
Discontinuous Piecewise Linear Functions
Intuitively, in a continuous piecewise linear function, the endpoint of one segment has
the same coordinates as the initial point of the next segment. There are piecewise
linear functions, however, where two consecutive breakpoints may have the same x
ILOG CPLEX C++ API 9.0 REFERENCE M ANUAL 228