simultaneous curve fitting using "fmincon"

Hi, I'm new with Optimazation function. I m trying to simultaneous fit more than 2 data set but using the same function with different parameters (11) among which 2 vary linearly. I also have to set a boundaries for this parameters according to physically acceptable value.

here is my code for 2 data set:

load E30_data.txt;

load E60_data.txt;

y30 = E30_data(:,2);

y60 = E60_data(:,2);

lambda = E30_data(:,1);

nonlcon = [];

lb = [0.001 1.55 0.002 24000 1000 2.1460 1000 1000 1.3545 1000 02562];

ub = [0.009 2.45 11.8 48000 4000 3.600 8756 5E11 1.90545 8965 6E11];

x0 = [0.004 1.99 2.8 39750 2850 2.8773 6880 2944683560 1.5251 7812 167964024];

options = optimset('Display','iter','MaxFunevals',4000,'TolFun',1e-10 ,'Algorithm','trust-region-reflective','GradObj','on');

fitfunc = @(c)fitfunction(c,y30,y60);

 parameter =fmincon(fitfunc,x0,[],[],[],[],lb,ub,nonlcon,options);

where the function fmincon is:

function error = fitfunction(c,y30,y60)

y1 = mie_extinction(c(1:11));

y2 = mie_extinction(c(12:22));

error = norm(y30 - y1') + norm(y60 - y2');

and the function mie_extinction help for theoretical calculation for y1 and y2.

By compiling my main code I have the error:

Error using fitfunction

Too many output arguments. Error in @(c)fitfunction(c,y30,y60)

Error in fmincon (line 649)

      [initVals.f,initVals.g] =
      feval(funfcn{3},X,varargin{:});

Error in demofitextinction_v200114 (line 55)

 parameter
 =fmincon(fitfunc,x0,[],[],[],[],lb,ub,nonlcon,options);

Caused by: Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.

I try my best solving this problem but I could'nt.

It would be a great help if someone can help me overcome this problem.

thanks in advance

Answer 1

[Amit]

This is because you have GradObj On but your function does not provide gradient vector.

Try something like this:

options = optimset('Display','iter','MaxFunevals',4000,'TolFun',1e-10 ,'Algorithm','interior-point');
fitfunc = @(c)fitfunction(c,y30,y60);
 parameter =fmincon(fitfunc,x0,[],[],[],[],lb,ub,nonlcon,options);

[RoDo]

Thanks Amit for your response. I eliminate GradObj and replace the algoritm by 'interior-point' as you sugested and it did'nt solve my problem, but it gave another error message like:

Index exceeds matrix dimensions.

Error in fitfunction (line 19)

y2 = mie_extinction(c(12:22));

Error in @(c)fitfunction(c,y30,y60)

Error in fmincon (line 640)

      initVals.f = feval(funfcn{3},X,varargin{:});

Error in demofitextinction_v200114 (line 54)

 parameter
 =fmincon(fitfunc,x0,[],[],[],[],lb,ub,nonlcon,options);

Caused by: Failure in initial user-supplied objective function evaluation. FMINCON cannot continue.

[Amit]

One thing that I see on first glance is, the c is suppose to be 22x1 size, however x0 (initial guess) is only 11x1 in size.

[RoDo]

x0 ist the start parameter. And c schoud be the output values corresponding to parameters, when y1 fits y30 (here with parameters c1 = c(1:11)) and y2 also fits y60 (here with parameters c2 = c(12:22)).

[Amit]

Thats what I am saying. that c is 22x1 vector and not 11x1. You are trying to optimize c using the initial values provided as x0. The dimensions of x0 and c should be same in order for fmincon to start.

[RoDo]

thanks a lot Amit.

By just enlarging the size of x0 to the same size like c, my program works. Now I just have to refine it to get the expected values.

Once again great thank!