MATLAB: Fixing a value inside the objective function while using FMINCON

fminconMATLABoptimization

Hi,

I am using 'fmincon' inside a script 'Script.m' optimizing the output of the function 'cost_simplified' based on the independent variable 'q' ( i have provided the code script). But while varying the values of 'q' I need to keep the value of a double which is dependent on 'q' i.e., 'X.pa' same as 'contact_points' which is a constant taken as input ( i.e. i need to satisfy 'X.pa==contact_points', and then proceed further inside the function 'cost_simplified').

How can i meet this constrain ('X.pa==contact_points') inside the objective function 'cost_simplified' ?

I have tried for 'if ~isequal(X.pa,contact_points) return end' . But using 'return' brings out the error "Output Argument "…" not assigned during call to "Script.m>cost_simplified". If i assign output argument to 'zero' , optimization algorithm 'fmincon' stops as the ouput 'zero' remains constant after every iteration.

nonlincon=@(q) graspcon(q,G,contact_points,Kc_new,X); %%% concept of extra parameters
[q{i},cost_val_new(i)]= fmincon (@(q) cost_simplified(w,yopt,q,G,contact_points,object.normals,mu,fmin,fmax,k,X,object),q0,A,b,Aeq,beq,lb,ub,nonlincon);

Best Answer

You should not try to abort your objective function just because you know that the q fmincon is in the process of evaluating doesn't satisfy intended constraints. Preventing fmincon from completing its evaluation of q is denying it the very information it needs to search for a solution.

Related Solutions

MATLAB: QP with quadratic constraints using fmincon

It might be a bit safer to formulate ceq differentiably

 ceq=norm(x)^2-1

You could also consider providing gradient calculations for the objective function and constraints, since the formulae for those are fairly simple.

Lastly, I would point out that the problem has a closed form solution, which you might consider if your problem dimension is not too large. Below is my implementation, though I warn you that it is fairly new and untried.

function [x,fval] = trustregprob(Q,b,w,doEquality)
%Solve trust region minimization problems using eigendecomposition
%




%   [x,J] = trustregprob(Q,b,w)
%   [x,J] = trustregprob(Q,b,w,doInequality)
%
%When doEquality=true (the default), solves
%
%   Minimize J(x) = x.'*Q*x/2-dot(b,x) such that |x| = w
%
%When doEquality=false, solves instead subject to |x|<=w
%
%Q is assumed symmetric, but not necessarily p.s.d. Since the solution is based on
%eigendecomposition, it is appropriate mainly for Q not too large. If multiple
%solutions exist, only one solution is returned.
if ~exist('doEquality','var')
   doEquality=true; 
end
if w<0, error 'Arguemnt ''w'' must be non-negative.'; end
if ~w
    x=zeros(size(b));x=x(:);
    fval=0;
    return
end
N=size(Q,1);
[V,H]=eig((Q+Q)/2);
h=diag(H);
posdefIneq=all(h>=0) & ~doEquality;
if ~isreal(h) || ~isreal(V),
    disp 'Q not symmetric?'
    keyboard; 
end
if ~any(b)
      if posdefIneq
        x=b; %all zeros  
      else
       [lambda,imin] = min(h);
        x=w*V(:,imin);
      end
      if nargout>1, fval=(x.'*(h.*x))/2; end
elseif posdefIneq
      Vt=V.';
      g=Vt*b;
      x=g./h;
      if norm(x)<w
          if nargout>1,
            fval=(x.'*(h.*x))/2 - dot(g,x);
          end
          x=V*x;
      else
          [x,fval]=  trustregprob(spdiags(h,0),g,w);
      end
else   
      %diagonalize
      Vt=V.';
      g=Vt*b;
      hmin=min(h);
      idx=logical(g);
      gnz=g(idx);
      hnz=h(idx);
      [him,im]=min(hnz);
       gim=gnz(im);
      fun=@(lambda) norm( gnz./(hnz-lambda) ) - w;
      ub=him-abs(gim)/w;
      i=0;
      lb=ub-10^i;
      while fun(lb)>=0
          i=i+1;
          lb=ub-10^i;
      end
      lambda=fzero(fun,[lb,ub]);
      if lambda>hmin
        x=g; 
        x(idx)=g(idx)./(h(idx)-hmin); 
       cc=w-norm(x)^2;
       nidx=~idx;
       nn=sum(nidx);  
       x(nidx)=sqrt(cc/nn);
      else
       x=g; 
       x(idx)=g(idx)./(h(idx)-lambda);
      end
      if nargout>1,
        fval=(x.'*(h.*x))/2 - dot(g,x);
      end
      x=V*x;
end

MATLAB: How to write Continue Long Statements on Multiple Lines

Use repmat to avoid manually typing all 160 of those ‘%q’ repeats!

Try this:

formatSpec = ['%f',repmat('%q',1,160), '%[^\n\r]'];

Related Question