Nonlinear Least Squares with Linear Equality

2015 10 18
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更新时间：2015 10 19
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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

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回答（1 个）

Walter Roberson
Walter Roberson 2015-10-19

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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.

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Kai Chung
Kai Chung 2015-10-19
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
Walter Roberson 2015-10-19
The default if you do not specify options is Interior Point, which is described in more detail here

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