How to plot the trajectory that fminsearch follows?

Question

Burak 2020-11-23

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/658023-how-to-plot-the-trajectory-that-fminsearch-follows

编辑： Burak 2020-11-23

I am trying to optimize rosenbrock's function with fminsearch and also drawing the point that gives the minimum value with point size being proportional to the iteration number at each iteration on the 2-D contour plot of rosenbrock's function, however that's not a good idea. As the point size gets bigger it's difficult to see other points. Instead I would like to plot the trajectory fminsearch follows so that I can see the path clearly. How would one do that?

I couldn't find a way to do it as you only get a single point passed to the `outputFcn`.

Here is my plot:

Here is an example of how I would like it to look like (just to clarify what I want):

options = optimset('outputFcn', @out, 'Display', 'iter');
x = [3.5    2.5     0.5     0.5];
y = [0      -2      -2      0];
[x,fval,eflag,output] = fminsearch(@rosenbrock_wrapper, [x(4), y(4)], options)
title 'Rosenbrock solution via fminsearch'
%Rosenbrock Function
function val = rosenbrock(x, y)
% a = 1.5, b = -1
val = (1 - x + 1.5) .^ 2 + 100 * (y + 1 - (x - 1.5) .^ 2) .^ 2;
end
%Rosenbrock Wrapper
function val = rosenbrock_wrapper(X)
val = rosenbrock(X(:, 1), X(:, 2));
end
%Output Function
function stop = out(x, optimValue, state)
stop = false;
switch state
    case 'init'
        fcontour(@rosenbrock, [0 3 -3 3], 'MeshDensity',50, 'LineWidth', 2, 'LevelList', 1:5:300);
        hold on;
    case 'iter'
        plot(x(1), x(2), '.', 'MarkerSize', optimValue.iteration + 1);
end
end

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Answer 1

Matt J 2020-11-23

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/658023-how-to-plot-the-trajectory-that-fminsearch-follows#answer_552803

编辑：Matt J 2020-11-23

在 MATLAB Online 中打开

trajectory=doIt();

fcontour(@rosenbrock, [0 3 -3 3],'LineColor', '#00FFFF', 'MeshDensity',50,...

'LineWidth', 2, 'LevelList', 1:25:300);

hold on

plot(trajectory(1,:),trajectory(2,:),'ks-','MarkerFaceColor','k')

plot(trajectory(1,end),trajectory(2,end),'ro','MarkerSize',20)

hold off

title 'Rosenbrock solution via fminsearch'

function history=doIt

options = optimset('outputFcn', @out, 'Display', 'none');

x = [3.5 2.5 0.5 0.5];

y = [0 -2 -2 0];

history=[];

[x,fval,eflag,output] = fminsearch(@rosenbrock_wrapper, [x(4), y(4)], options);

%Output Function

function stop = out(x, optimValue, state)

stop = false;

switch state

case 'iter'

history=[history,x(:)];

end

%Rosenbrock Function

function val = rosenbrock(x, y)

% a = 1.5, b = -1

val = (1 - x + 1.5) .^ 2 + 100 * (y + 1 - (x - 1.5) .^ 2) .^ 2;

end

%Rosenbrock Wrapper

function val = rosenbrock_wrapper(X)

val = rosenbrock(X(:, 1), X(:, 2));

end

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Burak 2020-11-23

编辑：Burak 2020-11-23

Just what I was looking for, thank you! I couldn't think of a way to do it by parameterization. Oh by the way, I just moved that plot part inside the output function in 'done' case.

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