MATLAB: Error in Rosenbrock Optimization with Analytic Hessian

Question

The following program is not working.

It is generating the following error:

 Error using gradient (line 6)
 Not enough input arguments.
 Error in rosenbrockwithgradhess (line 7)
        g = gradient(x);
 Error in Optimization_With_Analytic_Hessian>@(x)rosenbrockwithgradhess(x,
 double(a),double(b)) (line 27)
    [x, fval, eflag, output] = fminunc(@(x)rosenbrockwithgradhess(x, 
 double(a), double(b)), x0, options);
 Error in fminunc (line 280)
      [f,GRAD,HESS] = feval(funfcn{3},x,varargin{:});
 Error in Optimization_With_Analytic_Hessian (line 27)
     [x, fval, eflag, output] = fminunc(@(x)rosenbrockwithgradhess(x, 
 double(a), double(b)), x0, options);
 Error in main (line 57)
        [x, fval, eflag, iter, fcount] = 
 Optimization_With_Analytic_Hessian(starting_point);
 Caused by:
     Failure in initial user-supplied objective function evaluation. 
 FMINUNC cannot continue.

Optimization_With_Analytic_Hessian.m

 function [x, fval, eflag, iter, fcount] = 
 Optimization_With_Analytic_Hessian(start_point)
    %   assign start point
    x0 = start_point;
    %   read coefficients a, b
    coeff = load('coeff.txt');    
    a = coeff(1);
    b = coeff(2);
    % options setup
    options = optimoptions( 'fminunc', ...
                        'Display','off',...
                        'OutputFcn',@bananaout,...
                        'Algorithm','trust-region', ...
                        'GradObj','on',...
                        'Hessian', 'on');
    %   calling fminunc 
    [x, fval, eflag, output] = fminunc(@(x)rosenbrockwithgradhess(x, 
 double(a), double(b)), x0, options);
    iter = output.iterations;
    fcount = output.funcCount;    
    %   plot window title
    title 'Optimization with Analytic Hessian...'    
    disp('Optimization_With_Analytic_Hessian...');
end

Relevant Source Code:

 function [f, g, h] = rosenbrockwithgradhess(x, a, b)
    % Calculate objective f
    f = rosenbrock(x, a, b);  
    % gradient required
    if nargout > 1 
        g = gradient(x);
    end
    % hessian required
    if nargout > 2 
        h = hessian(x);
    end    
end

rosenbrock.m

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

gradient.m

 function out = gradient(coord, a, b )
    x = coord(1);
    y = coord(2);
    out = [2 *(-200 *(a - x) *(a^2 - 2*a*x + b + x^2 - y) - a + x - 1); 
            200 *(-(a - x)^2 - b + y)];
end

hessian.m

 function out = hessian(coord, a, b )
    x = coord(1);
    y = coord(2);
    out = 400 * (200 * (a-x)^2 + 200*b - 200*y + 1);
end

main.m

 function main()
    %   initial data
    points_count = 4;
    coeff_file_name = 'coeff.txt';
    start_points_file_name = 'data.txt';
    file_write_mode = 'w';   
    a = gen_const();% integer

    b = gen_const();% integer
     %   write coefficients to a file
    write_to_file(coeff_file_name, [a, b], file_write_mode)
    %   generate 4 random points
    m = gen_points(a, b, points_count);    
    %   write the points to a file
    write_to_file(start_points_file_name, m, file_write_mode);
    %   load points from file
    points = load(start_points_file_name);
    plot_ban();
    %   iterate through the points and use them in optimization    
    for i = 1:points_count
        starting_point = points(i,:);
        if i==1
            file_write_mode = 'w' ;
        else
            file_write_mode = 'a';        
        end
        %   Optimization with Analytic Hessian
        [x, fval, eflag, iter, fcount] = 
 Optimization_With_Analytic_Hessian(starting_point);
        write_to_file('Optimization_With_Analytic_Hessian.txt', 
 [a, b,starting_point, x, fval, eflag, iter, fcount], file_write_mode);
    end    
end

Answer 1

Your rosenbeckwitgradhess routine is receiving a and b as arguments but is not passing them to your gradient.m