Nelder-Mead algorithm
in [Matlab]
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From: Jan on 6 Jun 2010 11:32 Dear I use fminsearch (Nelder-Mead algorithm) as optimization algorithm in a non-linear least square peak fitting application. Now, I am investigating the algorithm, but the simplex method isn't very clear to me. Will this method generate new points (extrapolate) or just use the points from the function (curve)? Can sombody make this clear to me? Thanks in advance Jan
From: John D'Errico on 6 Jun 2010 13:28 "Jan " <jan_neyens(a)skynet.be> wrote in message <hugf1j$ib4$1(a)fred.mathworks.com>... > Dear > > I use fminsearch (Nelder-Mead algorithm) as optimization algorithm in a non-linear least square peak fitting application. > Now, I am investigating the algorithm, but the simplex method isn't very clear to me. Will this method generate new points (extrapolate) or just use the points from the function (curve)? > > Can sombody make this clear to me? Nelder-Mead has nothing to do with interpolation OR extrapolation, nor would any optimizer care about that. So I don't know what you are asking. You may wish to read about Nelder-Mead. http://en.wikipedia.org/wiki/Nelder–Mead_method John
From: Jan on 6 Jun 2010 16:27 Thanks for your reply But that is just the site from where I am doubting. They write: 'Nelder–Mead generates a new test position by extrapolating the behavior of the objective function measured at each test point arranged as a simplex.' So, from this text, I understand that they extrapolate the points of the curve. Can you please explain this for me.. Thanks in advance Jan
From: John D'Errico on 6 Jun 2010 19:43 "Jan " <jan_neyens(a)skynet.be> wrote in message <huh0ap$7sp$1(a)fred.mathworks.com>... > Thanks for your reply > > But that is just the site from where I am doubting. They write: 'Nelder–Mead generates a new test position by extrapolating the behavior of the objective function measured at each test point arranged as a simplex.' > > So, from this text, I understand that they extrapolate the points of the curve. > Can you please explain this for me.. NO! Nelder-Mead does not extrapolate points from a curve. I said this before, and I will repeat my statement. It chooses where to test the function at new trial points based on information from previous points, based on the presumption that where the function increases or decreases, it will continue to do so by looking further in a similar direction. Of course this is no different from any other optimization tool. Is this extrapolation? Not at all. Extrapolation PREDICTS a new value from prior ones. Nelder-Mead NEVER predicts a new value. It merely infers that the objective function will continue to behave in a relatively well-behaved manner. So that moving in the same direction where the function increases or decreases, the optimizer hopes to see more of the same behavior. This is not extrapolation, because prediction is never done, only inference that a function will continue to move in the same direction that it did before. John
From: Steven Lord on 6 Jun 2010 21:50
"Jan " <jan_neyens(a)skynet.be> wrote in message news:huh0ap$7sp$1(a)fred.mathworks.com... > Thanks for your reply > > But that is just the site from where I am doubting. They write: > 'Nelder–Mead generates a new test position by extrapolating the > behavior of the objective function measured at each test point arranged as > a simplex.' > > So, from this text, I understand that they extrapolate the points of the > curve. No. Nelder-Mean uses the values of the functions at points where it's previously evaluated the function to decide where to evaluate the function next. There's no extrapolation or interpolation involved -- simply evaluation. -- Steve Lord slord(a)mathworks.com comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ To contact Technical Support use the Contact Us link on http://www.mathworks.com |