Lsqnonlin : the initial values don't vary and Genetic Algo is too slow (791 variables)

Hello,

I am used to fminsearch (and fminsearchbnd provided by a User of this forum which works very well) but this time I need to minimize a function of 791 variables.

That's why I am trying the lsqnonlin. I have computed the function and not the Sum of the squared as the method requires it. The function is a sum from 1 to 39 so the function coded returns a column (39x1)

The issue is that lsqnonlin doesn't seem to make any variation from the initial values. I have tried other intial values and nothing changed.

[x,fval,exitflag,output]=lsqnonlin(@(x)ObjectiveStep5LSQ(x,SigmaS,k0,ZCcurve,gFunction,ag,bg,cg,dg,SwapLengths,Talpha,Tbeta,w,FwdIni,BetaS, ForwardSwapRate,delta_k),D,[],[],optimset('Display','iter-detailed','TolFun',10^-14,'TolX',10^-14,'MaxFunEvals',4000));

I have checked that the initial values are properly passed to the process and it is the case. Is there something I am missing ?

Additional information: In fact, it is a correlation matrix (39x39). Therefore I just need to calibrate the TriL without the diagonal as it has to be one. As initial guess I use exp(-b*abs(i-j)) with a given b. I couldn't put the boundaries conditions as each Function_k depends on 38 variables.

I have also tried the Genetic Algorithm (ga) and it seems to converge but it very very slow. I think it would take a week to complete (or not) the procedure.

Thank you for your help

Answer 1

[Matt J]

My guess is your objective function is piece-wise constant. Try making small changes mnaually to your initial guess and see if it changes the objective function value.

[Alan Weiss]

To expand on Matt's answer, you can try setting the DiffMinChange option to 1e-3 or something. But it might not work, depending on how wide the flat regions are.

Alan Weiss

MATLAB mathematical toolbox documentation

[Alicia]

Hello Matt.

Thank you for your help. Here is the value of the objective function for an initial correlation matrix with b=1 and for b=0.999.

b=1

0,114682115725103 0,122106163029283 0,124543223217477 0,126098357301418 0,122743801384779 0,116860547867268 0,114458349092582 0,112201022689827 0,114109958242459 0,117986335715620 0,115457115093831 0,112402804721648 0,928637870695923 0,908769660960317 0,105117952047035 0,103089990814102 0,101855821374688 0,101280712457875 0,100005732090886 0,0979686443680163 0,0946263526728049 0,0917830665168247 0,0883828692715365 0,0853085777545121 0,0826724949169561 0,0793807409708680 0,0764470350712997 0,0739044190743753 0,0709686641355847 0,0674081248211683 0,0645911005865177 0,0615415173945147 0,0582799442456101 0,0542800899336852 0,0495332131807206 0,0451994494354521 0,0379027385380122 0,0285428841561874 0,0166492080764459

b=0.999

0,114393600943569 0,121748347426660 0,124124925693462 0,125624926471981 0,122218860409478 0,116286742021568 0,113837634134796 0,111534902707084 0,113399603863839 0,117232651809618 0,114660777956751 0,111564295594162 0,927757499772531 0,907847585405903 0,104154226502043 0,102084550282370 0,100808523389251 0,100191356097318 0,0988740397542877 0,0967942802509965 0,0934092229293486 0,0905228957156798 0,0870792451675742 0,0839610454821423 0,0812807964675597 0,0779445770673584 0,0749664124811430 0,0723794388988339 0,0694000941647167 0,0657971632562833 0,0629402895304210 0,0598539267206838 0,0565591634000212 0,0525289209173312 0,0477549390495756 0,0433975402773964 0,0360956111374499 0,0267842590839936 0,0150860340133054

It doesn't seem to be piecewise constant ? But here, I changed all the initial values , is that what you wanted me to try ?

Thank you again.

Alicia

[Alicia]

Hi Alan,

Thank you for your help ! I have tried to set this option but unfortunately, Lsqnonlin is still very slow (I have also tried 1e-2 and 1e-1). The first step takes a very long time (still running). I show the value of the functions and it doesn't seem to change a lot. It looks like my objective function is very difficult to minimize ?

Thanks again

[Marylen Sun]

Hello, do you find a solution to your problem please?