"Matt J" wrote in message <firstname.lastname@example.org>... > "Toan Cao" <email@example.com> wrote in message > > If you know a global lower bound on F(x), say F_low, then the minimization problem is equivalent to > > min f(x)'.f(x) > > where > > f(x)=F(x)- f_low > > So, you could apply Levenberg-Marquardt and/or Gauss-Newton to the reformulated problem.
I don't think it is a good suggestion. (1) It make the code difficult to handle since f_low needs to be known. It squares the conditioning of the original problem, and thus all kinds of numerical difficulties become more prominent.
When levenberg-Markquardt or pseudo-newton method is developed, f(x) is usually taken as the local Jacobian of F. And this approximation is generally known and studied. The approximation can be applied on any F (only assumed to be differentiable).