MATLAB: Fminunc stopped because it cannot decrease the objective function along the current search direction.

Question

Hi, I'm trying to use fminunc function with the gradient but it doesn't work properly.

my start point is: [1.5;-2.5]

this is my objective function:

function [f, g, H] = rosenboth(x)
% Calculate objective f
a = 0.5;
b = -1.5;
f = (1 - x(1) + a)^2 + 100 * (x(2) - b - (x(1) - a)^2)^2;
if nargout > 1 % gradient required
    g = [2 * (-200 * (x(1) - 1) * (-x(1)^2 + 2 * x(1) + x(2)) + x(1) - 2);
        200 * (-x(1)^2 + 2 * x(1) + x(2))];
    
    if nargout > 2 % Hessian required
        H = [1200 * x(1)^2 - 2400 * x(1) - 400 * x(2) + 802, -400 * (x(1) - 1);
            -400 * (x(1) - 1), 200];  
    end
end

and that's the generated code from optimtool

function [x,fval,exitflag,output,grad,hessian] = fmin_gradient(x0,OptimalityTolerance_Data,StepTolerance_Data)
%% This is an auto generated MATLAB file from Optimization Tool.
%% Start with the default options
options = optimoptions('fminunc');
%% Modify options setting
options = optimoptions(options,'Display', 'off');
options = optimoptions(options,'OptimalityTolerance', OptimalityTolerance_Data);
options = optimoptions(options,'FunctionTolerance', OptimalityTolerance_Data);
options = optimoptions(options,'StepTolerance', StepTolerance_Data);
options = optimoptions(options,'PlotFcn', @optimplotfval);
options = optimoptions(options,'Algorithm', 'quasi-newton');
options = optimoptions(options,'SpecifyObjectiveGradient', true);
options = optimoptions(options,'Hessian', 'off');
[x,fval,exitflag,output,grad,hessian] = fminunc(@rosenboth,x0,options);
end

Answer 1

Please run with the CheckGradients option set to true. I think that you will find that you did not calculate the derivatives correctly.

Alan Weiss

MATLAB mathematical toolbox documentation