Nonlinear Least Squares with Linear Equality

Hi,

I have a nonlinear least squares problem I need to solve, but I have a linear equality constraint on my parameters: a + b + c = 1.

I have been using lsqnonlin so far, is it possible to have constraints?

I tried substituting c = 1 - a - b, but it does not hold the equality because say if lsqnonlin arrives at the solution a = 0.7 and b = 0.7, a + b + c ~= 1.

Thanks

Answer 1

[Walter Roberson]

lsqnonlin() and lsqcurvefit() can only have upper and lower bounds. lsqlin() allows linear constraints but it is only linear rather than non-linear

So... what you have to do is transform the objective to one that computes the sum of squares directly and use fmincon() to minimize the residual.

[Kai Chung]

Thank you, managed to get it to work with fmincon. I'll have to document the methods I used in a report. My draft report mentioned using levenberg marquardt algorithm, but I suppose this is no longer the case. Would you have any idea what this uses? Is it still least squares?

[Walter Roberson]

The default if you do not specify options is Interior Point, which is described in more detail here