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DFNLP
The solver DFNLP solves
nonlinear data fitting problems using a sequential quadratic programming method.
This package solves the following nonlinear data fitting problems.
Data Fitting Methods
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L1 - DATA FITTING
Minimize |F(1,X)| + ... + |F(L,X)|
by introducing L additional variables Z(1),...,Z(L) and L + L additional
inequality constraints, the above problem is transformed into a smooth
nonlinear programming problem, that is then solved by a sequential
quadratic programming algorithm.
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L2 - OR LEAST SQUARES DATA FITTING
Minimize F(1,X)^2 + ... + F(L,X)^2
The algorithm transform the above problem into an equivalent nonlinear
programming problem by introducing L additional variables Z(1),...,Z(L).
The new objective function is
H(X,Z) = 0.5*(Z(1)^2 + ... + Z(L)^2)
and L equality constraints of the form
F(J,X) - Z(J) = 0
are formulated, J = 1,...,L.
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MAXIMUM-NORM DATA FITTING
Minimize { Maximum {|F(I,X)| : I=1,...,L} }
The problem is transformed into a smooth nonlinear programming problem
by introducing one additional variable Z yielding the objective function
H(X,Z) = Z
and L + L additional inequality constraints of the form
-F(J,X) + Z >= 0 , J=1,...,L,
F(J,X) + Z >= 0 , J=1,...,L.
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MAXIMUM FUNCTION
Minimize { Maximum {F(I,X) : I=1,...,L} }
Similar to the model above, one additional variable X is introduced to get a
simple objective function of the type
H(X,Z) = Z
and L additional restrictions
-F(J,X) + Z >= 0 , J=1,...,L.
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