Nonlinear Programs - AMPL

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18______________________________________ ________________________________________ __________________Nonlinear ProgramsAlthough any model that violates the linearity rules of Chapter 8 is not linear , theterm Nonlinear program is traditionally used in a more narrow sense. For our purposesin this chapter, a Nonlinear program, like a linear program, has continuous (rather thaninteger or discrete) variables; the expressions in its objective and constraints need not belinear, but they must represent smooth functions. Intuitively, a smooth function ofone variable has a graph like that in Figure 18-1a, for which there is a well-defined slopeat every point; there are no jumps as in Figure 18-1b, or kinks as in Figure 18-1c.

SECTION 18.1 SOURCES OF NONLINEARITY. 393 with the nonnegative parameterssupply[i]and demand[i]representing the units either available or required at city i.