How to use lsqnonlin together with MultiStart?

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Alexandre 2014-12-7

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/165800-how-to-use-lsqnonlin-together-with-multistart

评论： Alan Weiss 2018-6-6

Hello,

Please, I would like to see how I can use lsqnonlin together with the MultiStart solver to search over many initial points automatically and find the global solution of the portfolio optimization problem below.

I am using lsqnonlin to solve the following system for the n-order vector w and the scalar lambda. There is only a lower bound constraint at 0 for each element of w (short-selling constraint).

      x0=[1/n*ones(n,1);1];
      lb=[zeros(n,1);0];
      [w phi]=lsqnonlin(@sub,x0,lb);
      function fcns=sub(x)
      w=x(1:n,1);
      lambda=x(n+1,1);
      fcns(1:n,1)=lambda^(-1)*covmat^(-1)*(meanbl-(vec1'*covmat^(-1)*vec1)^(-1)*(vec1'*covmat^(-1)*meanbl-lambda)*vec1)-w;
      fcns(n+1,1)=w'*meanbl+phi*sqrt(w'*covmat*wb)-H;

Where the scalars H and phi, the n-order vectors meanbl and vec1, and the nxn matrix covmat are known.

I did not really understand the example at http://www.mathworks.com/help/gads/multistart-using-lsqcurvefit-or-lsqnonlin.html where the local solver used with MultiStart is lsqcurvefit instead of lsqnonlin.

Thank you very much.

Best wishes.

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Answer 1

Alan Weiss 2014-12-8

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https://ww2.mathworks.cn/matlabcentral/answers/165800-how-to-use-lsqnonlin-together-with-multistart#answer_161701

在 MATLAB Online 中打开

First you need to figure out bounds on all the parameters w and lambda. In general, it is not enough to say that lb = zeros(n+1,1), you also need an upper bound vector.

Once you have that, you can set up your problem for MultiStart easily. You just need to put your problem into a problem structure using the createOptimProblem function:

 problem = createOptimProblem('lsqnonlin','x0',x0,'lb',lb,'ub',ub,'objective',@sub);
 ms = MultiStart;
 [x,fval,eflag,output,manymins] = run(ms,problem,50);

Alan Weiss

MATLAB mathematical toolbox documentation

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Manuel Fuelling 2018-6-6

在 MATLAB Online 中打开

f_root2d_schnittgeraden.m

I used your code like this:

lb=[-15,10,-4,-20,0,5,-20,-5,-5,-20,0,-10,-20,-20,-20,-20];    %lower Bound      
ub=[-5,18,4,-5,8,10,-5,0,2,-5,8,0,20,20,20,20];        %upper Bound  
x0 = [-10,14,0,-13,5,8,-13,-2,0,-13,5,-8,1,2,3,4];        %Startwerte  
f_schnittgeraden=...
    @(x)f_root2d_schnittgeraden(x,stzpkt,w,Kantenlaenge,Winkel);  
   problem = createOptimProblem...
       ('lsqnonlin','x0',x0,'lb',lb,'ub',ub,'f_schnittgeraden',@(x)f_root2d_schnittgeraden);
   ms = MultiStart;
   [x,fval,eflag,output,manymins] = run(ms,problem,50);

i get the following error message: Error using createOptimProblem (line 107) No field f_schnittgeraden exists for PROBLEM structure. Type "help createOptimProblem" for a list of valid fields for each solver.

Error in s2_Schliff_Bild_to_P_Matlab (line 45) problem = createOptimProblem...

Alan Weiss 2018-6-6

You probably mean that to be your objective function. The correct field name is 'objective'. In other words, replace 'f_schnittgeraden' with 'objective'.

Alan Weiss

MATLAB mathematical toolbox documentation

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