Argument passing issue.

I have a requirement that, I use the following modified Rosenbrock function,

where the coefficients a and b are to be read from a text file.

.

I tried the following,

 function out = rosenbrock(x)
    disp('rosenbrock()..........called');
    coeff = load('coeff.txt');
    a = coeff(1);
    b = coeff(2);
    xx = x(1);
    yy = x(2);

    out = (1 - xx + a)^2 + 100*(yy - b - (xx-a)^2)^2;
 end

But it is doing two things,

(1) Slowing down the performance of the optimization.

(2) The output is also not correct (the optimization isn't converging).

How can I solve this issue wile fulfilling my requirement?

Is it possible to pass the values of a and b as the arguments of rosenbrockwithgrad()?

Relevant Source Code

 function [x, fval, eflag, iter, fcount] = 
        Optimization_With_Analytic_Gradient(start_point)

    x0 = start_point;

    %   inline function defitions
    %fungrad = @(x)deal(fun(x),grad(x));

    % options setup
    options = optimoptions( 'fminunc', ...
                            'Display','off',...
                            'OutputFcn',@bananaout,...
                            'Algorithm','trust-region', ...
                            'GradObj','on');

    % calling fminunc
    [x, fval, eflag, output] = fminunc(@rosenbrockwithgrad, x0, options);
    iter = output.iterations;
    fcount = output.funcCount;

    %   plot window title
    title 'Rosenbrock with Analytic Gradient...'    

    disp('Optimization_With_Analytic_Gradient...');
end 

 function out = gradient( x )
    out = [-400*(x(2) - x(1)^2)*x(1) - 2*(1 - x(1)); 
            200*(x(2) - x(1)^2)];
end

 function [f,g] = rosenbrockwithgrad(x)
    % Calculate objective f
    f = rosenbrock(x);    
    if nargout > 1 % gradient required
        g = gradient(x);
    end
 end

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/matlab/math/parameterizing-functions.html

[Ba Ba Black Sheep!]

I am extremely sorry. I could't figure it out.

 rosenbrockwithgrad_p = @(x)[rosenbrock(x, a, b); 
                            (nargout > 1) * gradient(x)];

    % calling fminunc
    [x, fval, eflag, output] = fminunc(rosenbrockwithgrad_p, x0, options);

Could you please help?

[Walter Roberson]

   function [x, fval, eflag, iter, fcount] = 
          Optimization_With_Analytic_Gradient(start_point, a, b)

      x0 = start_point;

      % options setup
      options = optimoptions( 'fminunc', ...
                              'Display','off',...
                              'OutputFcn',@bananaout,...
                              'Algorithm','trust-region', ...
                              'GradObj','on');

      % calling fminunc
      [x, fval, eflag, output] = fminunc(@(x) rosenbrockwithgrad(x, a, b), x0, options);
      iter = output.iterations;
      fcount = output.funcCount;

      %   plot window title
      title 'Rosenbrock with Analytic Gradient...'    

      disp('Optimization_With_Analytic_Gradient...');
  end 

   function out = gradient( x, a, b )
      %this routine probably needs to be changed to take a and b into account
      out = [-400*(x(2) - x(1)^2)*x(1) - 2*(1 - x(1)); 
              200*(x(2) - x(1)^2)];
   end

   function [f,g] = rosenbrockwithgrad(x, a, b)
      % Calculate objective f
      f = rosenbrock(x, a, b);    
      if nargout > 1 % gradient required
          g = gradient(x, a, b);
      end
   end