Polyhedra

1. Linear Programs:

   A linear program (LP) is an optimization problem in standard form, in which all the functions involved are affine. The feasible set is thus a polyhedron, that is, an intersection of half-spaces.

2. Polyhedral function:

   Polyhedral functions are functions with a polyhedral epigraph, and include maxima or sums of maxima of linear or affine functions. Such functions can be minimized via LP.

3. Half-spaces: \

   A half-space is a set defined by a single affine inequality. Precisely, a half-space \(\in \mathbf{R}^n\) is a set of the form mathbf{H} = left{ x ~:~ a^Tx le b right}, where a in mathbf{R}^n, b in mathbf{R}. <!–

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