How can I solve a problem using Constrained Nonlinear Regression?

Hi there,

I would like to perform contrained nonlinear regression. The scenerios for constraints are:

1. Sum of parameters = n1 and each parameter < n2 (i.e. b1 + b2 + b3 = 2 and b1, b2, b3 < 1)
2. Sum of parameters = n1 and each parameter ≤ n2 (i.e. b1 + b2 + b3 = 2 and b1, b2, b3 ≤ 1)
3. Sum of parameters = n1 and n2 < each parameter < n3 (i.e. b1 + b2 + b3 = 2 and 0.5 < b1, b2, b3 < 1.5)
4. Sum of parameters = n1 and n2 ≤ each parameter ≤ n3 (i.e. b1 + b2 + b3 = 2 and 0.5 ≤ b1, b2, b3 ≤ 1.5)
5. Sum of parameters <, ≤, >, ≥ n1 or n1 <, ≤ sum of parameters <, ≤ n2 (i.e. b1 + b2 + b3 <, ≤, >, ≥ 2 or 0.5 <, ≤ b1 + b2 + b3 <, ≤ 1.5)
6. Or any other alternative, if there is any remaining :)

I know that Matlab provides lsqlin for constrained linear LSQ and lsqnonline for nonlinear case. Yet, I couldn't find how to introduce summation contraint into lsqnonlin, like Aeq and beq in lsqlin.

I would be more than happy, if someone can help.

Cheers,

M

[Bruno Luong]

No optimizer can handles strict inequalities such as < and >. Simply because it is "ill posed" minimization.

Just think about this simple example:

What is is minimum of x with the constraint x > 0?

Such probem has solution.

Answer 1

[John D'Errico]

Sorry. lsqnonlin cannot handle general equalty or inequality constraints. Only bound constraints, and while you do have bound constraints, you also have an equality constraint on the sum.

That means you will need to use a more general optimizer, probably FMINCON. It can handle any of the constraint classes you mention.

Just pass it the sum of squares of residuals that you compute as an objective.

[Melanie VT]

That's great. Thank you very much 🙏

[Melanie VT]

I just have one more problem. fmincon seems to be useful for me, yet I want sum of the estimated parameters to be a constant number, say b1 + b2 + b3 = 10. How am I supposed to do that?

[Alan Weiss]

fmincon allows linear equality constraints.

Alan Weiss

MATLAB mathematical toolbox documentation

[Melanie VT]

I made a misinterpretation beforehand. Problem solved. Thank you both. Really grateful...