When you specify the same point more than twice as you declare a piecewise linear function, you inadvertently create an isolated point. ILOG CPLEX does not support isolated points. When it encounters an isolated point in the declaration of a piecewise linear function, ILOG CPLEX issues a warning and ignores the isolated point. An isolated point may appear as a visible point in the graph of a discontinues piecewise linear function. For example, the point (3, 2) would be an isolated point in Figure 18.2 and consequently ignored by ILOG CPLEX. Isolated points may also be less conspicuously visible; for example, if the height of a step in a discontinuous piecewise linear function is 0 (zero), the isolated point overlaps with an endpoint of two other segments, and consequently, the isolated point will be ignored by ILOG CPLEX.
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