Fminspleas

Efficient nonlinear regression fitting using a constrained, partitioned least squares overlay to fmi

Description

I need to thank Duane Hanselman for suggesting this great idea.

Fminspleas is a simple nonlinear least squares tool that fits regression models of the form

Y = a1*f1(X,C) + a2*f2(X,C) + ... + an*fn(X,C)

X can be any array, so it works on multidimensional
problems, and C is the set of only intrinsically nonlinear parameters. f1, f2, etc., must return a column vector result, of the same length as Y.

Because the optimization (in this case, fminsearch) need only work on the intrinsically nonlinear parameters, far fewer function evaluations are required. The example I give in the help took only 32 function evaluations to estimate 2 linear parameters plus 1 nonlinear parameter, versus over 300 evaluations had I just called fminsearch directly.

Fminspleas now allows you to specify bound constraints on the nonlinear parameters only. I'll see about adding linear parameter constraints if there are requests.

Finally, fminspleas allows the user to supply a set of non-negative weights to the regression.

E-mail me with any problems or bugs.

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
fminsearchbnd, fminsearch interface, Optimization Tips and Tricks

• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other Files: fminspleas.m, ; license.txt

[John D'Errico]

I've already added constraints to the nonlinear parameters in the new version going up, plus cleaned up the documentation a bit.

[Duane Hanselman]

The best approach for solving optimization problems where there is a mixture of linear and nonlinear terms. Solve for the linear terms using linear least squares embedded inside a nonlinear optimizer for the nonlinear terms. This function is difficult to describe with simple help text alone, but well worth the effort required to use it.

[Benson Tsui]

when I tried to use f = {1, @(xdata, coef) exp(xdata*coef)};
It gives the 'identifier' error.
can you tell me what causes the problem?