# Can the Levenberg-Marquardt algorithm be used for minimization and not fitting

Can the Levenberg-Marquardt algorithm be used for minimization and not fitting?

Usually we input the derivative of the function we want to fit in the minimizer. Now if I assume I have an objective function $f(t;a,b,c)$ (which I want to minimize with respect to the parameters $a,b,c$). Then I would not see a way to input something equivalent to the derivatives that I input for fitting.

So what should I do in this case?

Why am I asking this question? I have developed some C++ code for fitting with Levenberg-Marquardt, and it's a piece of art that I don't want to lose by starting from scratch with a new minimizer.

What do you think?

## 2 Answers

The Levenberg-Marquardt method can be used to minimize any problem of the form: $\min f(x)=\sum_{i=1}^{m} f_{i}(x)^{2}$ However, if the objective functino to be minimized is not a sum of squares, then the method is no longer applicable.

• This is just... sad! Commented Nov 26, 2013 at 17:00
• "no longer applicable" may be a bit strong. Often, the method can still be applied. In practice, it may still be a reasonably fast approach, just not a guaranteed fool-proof one. Commented Jan 11, 2014 at 19:15

Take a look at the book by Nocedal and Wright, "Numerical Optimization", to see the Levenberg-Marquardt method in more context than just fitting.