Mixed Integer Nonlinear Programming

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Mixed integer nonlinear programs (MINLPs) arise in a wide range of applications and combine the difficulties of nonlinear optimization with integer programming. We can state a MINLP in general as

minimizex f(x)
subject to ci(x) = 0 for i \in E
c_i(x) \geq 0 for i \in I
x \geq 0
x_i \in Z for some i \in \{1,\ldots,n\}

where each ci(x) is a mapping from Rn to R, and E and I are index sets for inequality and equality constraints, respectively.

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