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NON LINEAL FRACTIONAL PROGRAMMING (applications :gear: (performance cup,…
NON LINEAL FRACTIONAL PROGRAMMING
estabilishes that
In a max problem the numerator
must be concave
In Min problem the denominator
must be convex
Consist of
Optimize the ratio of the function
subject to
a set of linear constraints
reforming the initial problem in
a linealy equivalent one
using
search of equivalences
parametrization
variable substitution
defined as
Non-linear programming math model in which the objective functions is a ratio of two functions
where
F(x) is concave
G(x) is convex
applications :gear:
performance cup
standard deviation of portfolio
profit on risk
maximum production
Algorithms
Heuristic algorithm
consist of
Linearize the radio of the
objetctive functions
z= F1(x)
F2(X)
Assuming the difference
of the functions F(x) and G(x)
Charnes and Cooper
consist of
Tansform the problem
into a linear one using
a substitution
Jagannathan
consist of
the partial derivate of the
denominator substracted
drom the numerator