# Can constraints on the parameters be imposed in NonlinearModelFit? [closed]

Hi I cannot figure out this from the documentation of this command. For example, take one of the examples in the documentation, where I also added initial guesses for the parameters.

data = {{6.47, 3.65}, {7.43,
3.45}, {3.9, -2.94}, {4.8, -1.29}, {2.48, -0.35}, {6.32,
3.16}, {2.59, -1.19}, {9.13, -2.}, {3.81, -3.04}, {3.33, -2.68}}; \
Clear[model];
model[a_?NumberQ, b_?NumberQ,
c_?NumberQ] :=  (model[a, b, c] =
Module[{y, x},
First[y /.
NDSolve[{y''[x] + a y[x] == 0, y[0] == b, y'[0] == c},
y, {x, 0, 10}]]])

nlm = NonlinearModelFit[data,
model[a, b, c][x], {{a, 1}, {b, 2}, {c, 2}}, x,
Plot[nlm[x], {x, 0, 10}, PlotStyle -> Orange]]


Next, suppose I want to change the initial guesses to constraints $$a \in [1,1.5]$$, etc . My first guess does not work

nlm1 = NonlinearModelFit[data,
model[a, b, c][x], {{a, 1,1.5}, {b, 2,2.5}, {c, 2,3}}, x,

• Constraints are added in the "model" section of the command: NonlinearModelFit[data, {form, cons}, {β1, …}, {x1, …}]. cons are your constraints. It's the third headline example in the documentation. Feb 14 at 14:53
• As shown in the documentation, "NonlinearModelFit[data, {form, cons}, {[Beta]1, ...}, {x1, ...}] constructs a nonlinear model subject to the parameter constraints cons." Group the constraints with the model. Feb 14 at 14:53

A simple F1 would have shown the following.

NonlinearModelFit[data,{form,cons},{β1,…},{x1,…}] constructs a nonlinear model subject to the parameter constraints cons.

With examples like

NonlinearModelFit[data, {Log[a + b x^2], a > 0 && b > 0}, {a, b}, x,
Method -> "InteriorPoint"]


nlm = NonlinearModelFit[
data
, {
model[a, b, c][x],
1 < a < 1.5
}
, {{a, 1}, {b, 2}, {c, 2}}
, x
];


Beware that Method -> "Gradient" is incompatible with constrains. You may get the error

Gradient can only be used for unconstrained problems. NonlinearModelFit::ucmtd: Method -> Gradient can only be used for unconstrained problem