
Re: Nonlinear optimization
Posted:
Mar 5, 2013 2:26 AM


"Matt J" wrote in message <kh32ds$hrn$1@newscl01ah.mathworks.com>... > "Toan Cao" <toancv3010@gmail.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 LevenbergMarquardt and/or GaussNewton 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 levenbergMarkquardt or pseudonewton 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).
Bruno

