Mixed-integer linear programming

Author: ILOG
Method: <a href="/ddwiki/index.php?title=Simplex&amp;action=edit" class="new" title="Simplex">Simplex + <a href="/ddwiki/index.php?title=Barrier_methods&amp;action=edit" class="new" title="Barrier methods">barrier methods

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Mixed-integer linear programming (MILP) refers to optimization problems of the form:

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

where $f(\mathbf{x,y})$ , $\mathbf{g(x,y)}$ and $\mathbf{h(x,y)}$ are all affine functions of the vectors $\mathbf{x}$ and $\mathbf{y}$ , $n$ and $m$ are positive integers, and $\mathcal{Z}$ is the set of integers.