Linear-fractional programming
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In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear-fractional program in which the denominator is the constant function 1.
Formally, a linear-fractional program is defined as the problem of maximizing (or minimizing) a ratio of affine functions over a polyhedron,
where represents the vector of variables to be determined,
and
are vectors of (known) coefficients,
is a (known) matrix of coefficients and
are constants. The constraints have to restrict the feasible region to
, i.e. the region on which the denominator is positive.[1][2] Alternatively, the denominator of the objective function has to be strictly negative in the entire feasible region.