Integer nonlinear programming

From DDWiki

Nonlinear programming refers to optimization problems of the form:

minimize	$f(\mathbf{x})$
with respect to	$\mathbf{x}$
subject to	$\mathbf{g(x) \leq 0}$
	$\mathbf{h(x)=0}$
	$\mathbf{x}\in\mathcal{Z}^n$

where $n$ is a positive integer and $\mathcal{Z}$ is the set of integers. If $f(\mathbf{x})$ and $\mathbf{g(x)}$ are convex functions of the vector $\mathbf{x}$ and $\mathbf{h(x)}$ is an affine function of the vector $\mathbf{x}$ , then the problem is a convex INLP (an important subclass of INLPs).