Transcription of Nonlinear Programs - AMPL
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Example: air traffic controller
Nonlinear Programs - AMPL
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. Mathe-matically, a smooth function of any number of variables must be continuous and musthave a well-defined gradient (vector of first derivatives) at every point; Figures 18-1b and18-1c exhibit points at which a function is discontinuous and nondifferentiable, problems in functions of this kind have been singled out for several rea-sons: because they are readily distinguished from other not
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.
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