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Re: Which optimization method to use?
Posted:
Mar 28, 2013 11:23 AM


Alan_Weiss <aweiss@mathworks.com> wrote in message <kj1dck$hh5$1@newscl01ah.mathworks.com>... > On 3/27/2013 1:09 PM, Aino wrote: > > Hello all. > > > > I have a function that includes a simulation. The input of the > > simulation is seven parameters. I need to vary five of the seven > > parameters to find the combination that would minimize the final > > output (error that is calculated between a measured signal and the > > simulated signal). I have somewhat a good initial guess for the five > > parameters and I know that they should all be positive. I need to do > > this optimization several times, so computational cost is an issue too. > > > > I tried the optimization with "fminsearch". It worked quite ok, but > > two problems still occurred. First, one of the five parameters had > > negative values. This particular parameter is possible to just leave > > out. Second, it would seem that there are several local minimum that > > are all feasible when considering the parameter values :( and > > "fminsearch" didn't always find the global minimum. Also, I think that > > the output error includes "noise", or maybe one/several parameters are > > not always relevant. > > I am now trying out "fminsearchbnd" (File Exchange) without the fifth > > parameter and with lower bounds [0,0,0,0]. However, I was wondering if > > "fmincon" would be more appropriate for me? I am not sure how to > > implement it, though. Is there possibly even better (more robust, not > > too timeconsuming) optimization method for me? > > > > Thanks, > > Aino > > You might be interested in the documentation on optimizing simulations: > http://www.mathworks.com/help/optim/ug/optimizingasimulationorordinarydifferentialequation.html > > fmincon is indeed an appropriate solver for your problem. It is part of > Optimization Toolbox. You should use the interiorpoint or sqp > algorithms; see > http://www.mathworks.com/help/optim/ug/writingconstraints.html#br9p_ry > > Alan Weiss > MATLAB mathematical toolbox documentation
Thank you for your answer!
I am now testing the "fmincon" with "sqp". I still have some questions about the optimization.. First, I don't know exactly the whole parameter space (therefore I use only the "0" lower bounds and "Inf" higher bounds) and with bad parameters the simulation stops and gives something rather arbitrary for the error. I tried to put "NaN" as the error when the simulation stops, but "sqp" algorithm doesn't seem to know how to deal with the "NaN". Did I misunderstand the last part of your first link, about returning "NaN"? I get the following error statement:
"Objective function is undefined at initial point. Fmincon cannot continue."
Also, I would be happy with an error smaller than 0.05, is that what "TolFun" is for? I didn't see any difference between TolFun=0.1 and TolFun=0.05. Also, to speed the optimization, I would like to have a minimum step size for the input parameters. "DiffMinChange"? Setting DiffMinChange=0.01 lead to slower computing but also smaller error. Also, the parameters have a very different magnitude, is it possible to tweak the step size separately for each parameter? I have to say I'm a bit lost with this optimization.
Aino



